Probability

• Choosing a Duet, Lead Singer/Backup [Bryan, 02/25/2002]
  Twenty singers are trying out for a musical. In how many different ways can the director choose a duet? In how many ways can the director choose a lead singer and a backup?

• Conditional Probability [Black, 07/18/1998]
  What is the difference between drawing a blue marble conditional on drawing a red marble, and drawing a red-blue combination of marbles?

• Drawing Marbles [Kayla, 02/01/1997]
  A jar contains 2 red, 3 blue, and 4 green marbles. Niki draws one marble from the jar, and then Tom draws a marble. What is the probability that Niki will draw a green marble and Tom will draw a blue marble?

• An Explanation of Pascal's Triangle [Dortman, 2/27/1995]
  My 10th grade daughter is having trouble finding a simple explanation of Pascal's Triangle and its application.

• Fibonacci and Incoming Bits [Suja, 09/08/99]
  Given a transmitter sending 100 bits of random data over an ideal communication channel, what is the probability that there will be three consecutive 1's at least once in the sequence?

• Geodesics [Matz, 12/15/1996]
  Can you give me information on the math behind geodesics?

• Independent and Dependent Events [Kerry, 08/16/1998]
  How do I find the probability of independent and dependent events? Can you explain the difference?

• Line Segments and Size of Infinites [Allen, 03/19/1997]
  Divide a line segment into three parts, one half and one a quarter the length of the line segment. Choose a point at random along this line segment. What is that probability that this point lands in the 1/2 segment...?

• Math Symbol for C [Valovcin, 12/15/1997]
  I am puzzled by one symbol of typing math. What does the upper case letter C mean? As in (2C1) (3C1) / (47C2) = 6/1081.

• Montana Duck Hunters [Nanette, 11/27/2001]
  Montana duck hunters area all perfect shots. Ten of them are in a duck blind when 10 ducks fly over. All 10 pick a duck at random to shoot at, and all 10 fire at the same time. How many ducks could be expected to escape, on average, if this experiment were repeated a large number of times?

• Odds and Probability [Adrisch, 02/06/1997]
  Is "odds" slang for probability?

• Odds vs. Probability [Peace, 12/06/1996]
  What's the probability that a man can draw the numbers 2 and 7 from a hat containing the numbers 1-8?

• Powerball Lottery: Odds of Winning a Prize [Joshua, 09/02/2001]
  How are the Powerball lottery odds established?

• Probability and Genetics [Shirley, 12/30/2001]
  I am doing a math paper on Huntington's Disease. What does probability have to do with genetics?

• Probability of Being Born on Monday [Ferra, 8/26/1996]
  What is the probability that of any seven persons exactly one was born on a Monday?

• Probability of Hitting Safely [Jacob, 11/06/2001]
  Calculate the probability that a baseball player batting .357 would hit safely in at least 56 straight games, during the course of a 162-game regular season, assuming 4 at bats per game.

• Probability of Two Dice Summing to 5 [Yuxiao, 09/22/2001]
  If a person rolls two dice, what is the probability of getting a five as the sum?

• One Person of Seven Born on Monday [Ferra, 8/30/1996]
  If there is a 14 percent chance that any person selected at random was born on Monday, what is the probability that, of any seven people selected at random, exactly one was born on Monday?

• Poker Hand Odds [Kamanitz, 08/07/1997]
  What are the odds of getting exactly one pair in five card stud poker, using one 52-card deck?

• Probabilidad de que Juan y María se encuentren [Mora, 6/27/1996]
  Juan y María quedan a encontrarse entre las 7:00 y 8:00 en un Club...

• Probability: Let's Make a Deal [Gordon, 4/29/1996]
  Should the contestant stick with the original choice of doors or switch and choose the other door? What about the lottery?

• Probability of Rolling a 6 on One Die [Cantalupo, 4/30/1995]
  The following questions came up during a game of Risk...

• Probability of Two Male Children [McClory, 7/5/1996]
  If a family has two children, and the older child is a boy, there is a 50 percent chance the family will have two boys. However...

• A Truel [Zechiel, 3/6/1995]
  You and two of your friends get into a dispute and decide to solve it with a "Truel", a three way duel...

• When to Add, When to Multiply? [Aliza, 10/30/2001]
  When do you add and when do you multiply to compute probability?

• Why Add Probabilities in an OR Statement? [Mike, 05/25/1999]
  Why when we want to find the probability of, for example, rolling a 2 or 3 on a die, we add the number of twos and threes?

• Monty Hall Strikes Again [Pryor, 11/2/1994]
  There are three cups, one of which is covering a coin. I know the whereabouts of the coin, but you don't. You pick a cup, and I take one of the remaining cups, one which DOESN'T contain a coin. Both you and I know the cup I pick doesn't contain a coin. You then have the option to swap your cup with the third, remaining cup, or keep your first choice. What is the probability of the coin being in the cup if you keep your first choice, or if you decide to swap them?

• 30 hat probability question [Gong, 11/7/1994]
  In a department store there are 30 cubbies of different hats. Each hat has its own assigned cubbie box. However, there was an earthquake...

• Chances of Winning a Raffle [DiBianco, 2/15/1995]
  There is a concert and tickets are to be raffled off. There are 3500 winners and 175,000 applicants. I sent in 100 applications. What are my chances of winning?

• Advanced Probability as Used in a MAGIC [Denis, 2/15/1995]
  A MAGIC deck is composed of numerous subsets of cards that fall into specific categories. A card can be in several categories, but that isn't part of this problem. We would like to know how to calculate the probability of having pulled a card from a subgroup in the deck by the Xth turn, where X increases from 1 to whatever.

• The Probability of Outcomes [BilFred, 2/20/1995]
  In the sample space for a probability experiment, outcome A is twice as likly as outcome B. Outcome C is two-thirds as likely as outcome B. Outcome C is twice as likely as outcome D. Find the probability of each outcome in the sample space.

• A Geometry and a Logic Problem [Marsville, 3/11/1995]
  Problem 1: A cylindrical hole six inches long is drilled straight through the center of a solid sphere. What is the volume remaining in the sphere? Problem 2: The classical stay-switch problem.

• The Probability of Getting Dealt 4-of-a-kind [Hellen, 3/21/1995]
  What is the probablitiy of being dealt 5 cards and getting four of a kind?

• Are They Wearing Seatbelts? [Quinlab, 3/26/1995]
  80 percent of all California drivers wear seat belts. If 4 drivers were pulled over, what is the probability that all 4 would be wearing their seat belts?

• Probability of the Same Birthday within a Group [Bromley, 8/22/1995]
  What is the probability that, in a room of 30 people, two people will have the same birthday?

• Probability of Being Struck by Lightning [Vennebush, 8/23/1995]
  While all 3.4 million secretaries were at the annual secretaries' day picnic, a vicious storm began. Lightning headed directly for the secretaries. Given that males are eight times as likely to be hit by lightning as females, what is the probability that one of the male secretaries will be struck?

• Counting Handshakes [Lohr, 9/7/1995]
  There are 20 people in a room, and each person shakes hands just once with everyone else. Wouldn't this be 380 total handshakes? 19 * 20 = 380.

• Chocolate Chip Probability Word Problem [Lannin, 9/14/1995]
  Given 12 chocolate cookies there are 7 chocolate chips that are randomly placed into the cookies. What is the probability that at least one cookie has at least two chips?

• Probability That a Function Has Real Roots [Reichel, 9/24/1995]
  If r and s are numbers between 0 and 9, inclusive, what is the probability, P, that the function f(x) = x2 +rx + s has real roots? This question will consider only the case where r and s are integers.

• Tying Up Loose Ends to Create Different Size Loops [Taylor, 10/3/1995]
  Wandelina has six identical pieces of string held firmly in her fist, with one end of each sticking out above her fist, and the other end of each sticking out below her fist. Different people come along and tie the ends above her hand together, and tie the ends below her hand together. When Wandelina opens her fist and looks at the strings, what combinations of different size loops might there be? What is the probability of each possible combination occurring?

• Probability of Winning a Solitaire Game [Tsjrg, 10/26/1995]
  I am interested in finding out how to figure the probability of winning the solitaire 'clock game'.

• Probability for Correctly Guessing a Random Color [Martin, 11/16/1995]
  There are six choices for a color I'm thinking of. Someone guessed my color correctly, and then guessed again. She guessed correctly the second time and did this again, and again, and again, and again. What is the probability of this happening - that someone could guess correctly in a row?

• Probability that 6 Peas will Sink [Means, 1/23/1996]
  We need to know the probability that all six of these durn peas will be floating on top of the water before they are all six sunk down to the bottom of the jug...

• Assigning Committees using Probability [Hendershot, 2/7/1996]
  If a committee of 5 people is to be chosen from 12 couples with the restriction that no husband and wife can be on the same committee, how many possible committees are there?

• Probability in Flipping Coins [Kay, 2/25/1996]
  Six pennies are flipped. What is the probability of getting two heads and four tails? Etc.

• Probability of Picking in the Correct Order [Damour, 4/12/1996]
  Out of a population of 200 different amino acids, what is the probability of selecting the correct 20 acids in the correct order on your first try.

• Probability: 8-sided die [Charlton, 4/25/1996]
  I have an octahedron - what's the probability I'll roll a seven?

• Defining Probability [Knox, 4/30/1996]
  Is a probability number equal to a percent or a decimal?

• Probability of a Straight Flush [Mabbott, 5/15/1996]
  Finding the probability of drawing 5 spades, that is P(a flush) = (13 12 11 10 9)/(52 51 50 49 48) P(flush of any suit) = 4 P(a flush): the question is, what does the P(Straight flush) = ?

• Finding Probability on the Web [Arieh, 5/15/1996]
  I need a good history of probability, theory and basic concepts.

• Probability of Winning Roulette [Robbins, 5/16/1996]
  How can we calculate, discuss, and demonstrate the probabilities and mathematical expectations of roulette?

• Lottery Permutations [Dellinger, 5/16/1996]
  Determine the number of unique permutations of a lottery where you pick 6 numbers out of 49, and numbers may not repeat...

• Riemann, Mayan Math, Probability [Rob, 5/20/1996]
  Math projects: A. Riemann - a German mathmatician; B. The Mayan number system and calendar; C. Probability.

• Baccarat; a Casino Game [Robbins, 5/22/1996]
  Information on the probabilities of baccarat.

• Card Game Probability Question [Fred, 5/22/1996]
  What is the probability of getting a spade, queen and diamond

• Craps [Mike, 5/24/1996]
  Can you give me information on the probability and outcome of the game craps?

• Card Game Probabilities [Funk, 5/25/1996]
  What is the probability of getting two of a kind in a five-card Poker hand?

• Slot Machines [Robbins, 5/29/1996]
  What are the probabilities and mathematical expectations of slot machines?

• Probability of Drawing an Ace [Nstn, 5/31/1996]
  If I had 40 cards and there were 4 aces in the deck...

• Probability: Five and Seven Card Stud [Staas, 6/7/1996]
  We are trying to figure out how to calculate the probability of getting two pair and three of a kind in five and seven card stud.

• Random Card Shuffling Probabilities [Brasher, 6/11/1996]
  What is the probability of at least two eights being next to each other in a random shuffling of a deck of cards. What about at least two cards (2 eights or 2 queens etc.) being next to each other?

• Normal Distribution [SimonFlack, 6/24/1996]
  In six successive independent 'triple jumps' what is the probability that at least one total distance will exceed 18 meters?

• Probability in Craps Game [Richard, 6/27/1996]
  Find the probability that the shooter will win in a game of craps.

• Dice: Full House [Eastman, 6/28/1996]
  What is the probability of rolling a full house with 5 six-sided dice?

• Poker with a Pinochle Deck [Castill, 6/30/1996]
  What is the chance that a 5-card hand is a full house?

• Odds of Identical Numbers [Smith, 7/1/1996]
  How do you figure the odds of rolling the identical number on 6 dice in one roll?

• Poker With a Pinocle Deck [Jgracia, 7/1/1996]
  If we are playing poker with a pinochle deck, what is the probability that we can be dealt a full house?

• Probability of Getting a Job [Jolie, 7/10/1996]
  If there are 5 different jobs, and a person has a ten percent chance of getting any one job, what is the chance of getting any job at all?

• Probability that a Random Integer... [Anderson, 7/18/1996]
  How do I figure out the the probability that an integer chosen randomly would be an integer multiple of a given integer "n" ... or the probability that it would be a multiple of 2...7, and so on...?

• Full House in Draw Poker [Ludwig, 7/28/1996]
  A player is dealt 5 cards - a pair of aces and three other unpaired cards. What is the probability of winding up with a full house...

• Theory of 'Runs' [Brasher, 8/20/1996]
  If all possible orders of 20 people are considered, what is the average value of the number of places in the row...?

• Probability Tree Diagrams [Carter, 8/22/1996]
  What are the odds that two children will both be boys, firing once will hit a target, cargoes will arrive ruined?

• Binomial Distribution [Chuin, 8/25/1996]
  The mean life of a certain television tube is 1200 hours with a standard deviation of 200 hours... The probability that three machines will be in use on any one day is 0.8,0.7 and 0.6 respectively.

• Odds of Left-Handedness in a Group [Gallagher, 9/2/1996]
  Assuming that 10 percent of the population is left-handed, what are the chances of having 7 lefties in a class of 23 children?

• 2-Digit Number is Multiple of 14 [Railrodder, 9/10/1996]
  What is the probability that a randomly selected two-digit number is a multiple of 14?

• Similar Phone Numbers [Opper, 10/21/1996]
  What is the probability that two telephone numbers will contain the same numbers but in a different order?

• Combinations of Married Couples [Chu, 11/08/1996]
  What is the probability that 12 people can be grouped into 6 pairs where each pair is a married couple?

• SAT Probability Problems [Mike, 11/12/1996]
  What is the best way to solve probability problems on the SAT?

• Executive Committee Vote [Cooke, 01/21/1997]
  124 delegates must elect a 13-member executive committee from a list of 26 candidates. If each delegate votes for 10 candidates, what is the least number of votes a candidate can get and be elected?

• Winning the Lottery [Zink, 01/30/1997]
  Can you find a formula that predicts the outcome of the lottery?

• Probability of Independent Events [LaGrassa, 02/07/1997]
  If the probability of an event is known, is there a formula that will gives the probability of that event after a given number of trials?

• Neighboring Cards [Christopher, 02/18/1997]
  If you pick any two cards and then go look for them in the deck, what is the probability that you will find them next to each other?

• Questions of Probability [Foley, 03/22/1997]
  Questions concerning probability, Venn diagrams, marbles, acorns, dice, and bands.

• Point in a Circle [Zolnierz, 04/29/1997]
  Given a circle with two 6-inch chords running across the top and the bottom... find the probability that a point chosen at random is in the region between the chords.

• Intriguing Limit [Oliver, 04/30/1997]
  Why is the following true: lim x --> oo (1-1/x)^x = 1/e?

• Picking Colored Balls [Connie, 05/05/1997]
  A bag contains an assortment of red and blue balls. Given the probabilities of picking certain combinations of balls, determine how many red and blue balls are in the bag.

• Multiple Choice Tests [Nancy, 05/06/1997]
  If you have a test with 6 questions and 4 possible answers to each question and you guess all answers, what is the probability of getting all 6 questions right?

• Checking Account Balance [Grove, 05/08/1997]
  Each of your parents writes you a check for a random amount less than $400. What is the probability that more than $80 will remain in their joint account after the checks have been written?

• Drunk Drivers and Traffic Deaths [Kdhd, 05/14/1997]
  Knowing the total traffic fatalities and the number involving alcohol, what is the probability that a traffic death may be attributed to drinking...?

• Probability: Marbles, Coins, Cards [Berard, 05/24/1997]
  A series of questions about probability, permutations, and combinations.

• Card Hands [Nguyen, 05/26/1997]
  What is the probability of getting a straight, a royal straight, or a royal flush?

• Banana Stickers [Nathan, 05/29/1997]
  Each banana sticker has a different letter (A-Z). If you collect n stickers, what is the probability that you'll have all 26 letters?

• Binomial Distribution and Probability [Clarke, 06/07/1997]
  How does the binomial distribution relate to probability?

• The First Ace [Klinow, 06/12/1997]
  An ordinary bridge deck of 52 cards is thoroughly shuffled. The cards are then dealt face up, one at a time, until an ace appears. What is the probability that the first ace appears at the kth card or sooner?

• Picking the Same Ball [Guy, 07/07/1997]
  One ball is selected at random each day from a jar filled with balls. What are the odds you will randomly select the same ball two days in a row?

• Patterns in Pascal's Triangle [Luong, 07/21/1997]
  I am working on a project about Pascal's triangle trying to find as many patterns as I can and prove them by induction.

• Test for Tuberculosis [Strickland, 07/28/1997]
  A for tuberculosis was given to 1000 subjects, 8 percent of whom were known to have tuberculosis... what is the probability of a randomly selected person having tuberculosis...?

• Complex Ratio Problem [JDJ, 07/31/1997]
  If you randomly throw 3 points on a plane, you get a triangle... What is the probablilty that the triangle will become obtuse...?

• Survey Respondents Flip Coins [Sadie, 08/04/1997]
  Survey respondents are asked to flip a coin in private and answer question A if the result is a head and question B if the result is a tail... what's the probability that Question A will be answered "Yes"?

• Multiple Choice Test: Binomial Probability [Lauer, 08/05/1997]
  A multiple choice test consists of 9 questions with 5 choices for each answer...

• Figuring the Odds of 3 Cards [Ponder, 08/07/1997]
  In the card game Super Seven, how do you figure the odds against you of receiving three sevens?

• Roulette Betting "System" [Connie, 08/07/1997]
  One roulette system is to bet $1 on black. If black comes up on the first spin of the wheel, you win $1 and the game is over...

• Marbles and Dice [Connie, 08/07/1997]
  What is the probability that from three black and one red marble in a jar, one red and one black marble will be picked without replacing the marbles? Two ordinary dice are thrown. What is the probability that the sum will be six or at least one of the two faces will be odd?

• Should You Play? [Connie, 08/07/1997]
  A game consists of three cuts with a deck of 52 cards. You win $1 if a face card turns up on at least one cut, but you lose $1 if one does not turn up. Should you play?

• Ordering Probabilities [Hunter, 08/13/1997]
  The proportion of people who order coffee with their dinner is .9. A simple random sample of 144 patrons of a restaurant is taken...

• More Living or Dead? [Zifkin, 08/14/1997]
  Are there more people living now than have ever died?

• Raffle Tickets [Mostyn, 08/20/1997]
  A man buys 5 tickets in a 100-ticket raffle. There are three prizes...

• NCAA Lottery Formula [Cott, 08/27/1997]
  I have forgotten the formula for this probabilities/odds question about the lottery...

• Stolen Base [MinhVu, 08/29/1997]
  I need to create a mathematical model for a stolen base...

• The Two Envelopes [Becker, 09/08/1997]
  Given two sealed envelopes, one containing twice as much money as the other...

• Triangle Inequality [Joe, 09/14/1997]
  Suppose that you have a straight pipe cleaner of a given length. The two ends are points A and C...

• Throwing Dice More Than Once [Merjanian, 09/25/1997]
  If I throw one die once the probability of getting any one of the six numbers is 1/6. Does this change if I throw more than once?

• Bubble Gum Cards [Skrine, 09/28/1997]
  The bubble gum company decides to promote its gum by including in each pack the photo of one of six rock music stars...

• Paychecks and Envelopes [Martin, 10/07/1997]
  Five paychecks and envelopes are addressed to five different people...

• Selecting a Student Council [Bhavika, 10/08/1997]
  What is the probability of a student being selected in each of the following cases...?

• Probability Distributions [Dominic, 11/04/1997]
  Supposing a million people, without reference to each other's choices, each choose a 'random' number between 1 and 1,000,000...

• Poker, Probability, Combinatorics [Hundal, 11/04/1997]
  If we deal n hands consisting of 2 cards each, what is the probability that there will be no pairs amoung the hands?

• Average Time for a Mouse to Find Cheese [Shalit, 11/05/1997]
  A mouse has three rooms to go into...

• What's the Probability That Two Will Agree? [Hawkins, 11/10/1997]
  Of the nine members of the board of trustees of a college, five agree with the president. The president selects three trustees at random and asks their opinions...

• Line through a Disc, Terminating Zeros [Nodarse, 12/03/1997]
  1. A circular disc contains 2 billion randomly situated points. Can a straight line pass through the disc and have exactly 1 billion points on each side? 2. Find the terminating zeros in the standard numeral 580!

• Roulette Probability [Crow, 12/07/1997]
  What is the probability of winning a certain amount of money using only the even money bets and the two to one bets?

• Birthday Probabilities [Fred, 12/09/1997]
  What's the minimum number of people you need in order for the probability that two of them were born on the same day of the week to be 50 percent?

• Expected Value [Nesser, 12/09/1997]
  What is expected value?

• Probability of a Triangle [Kwiatkowski, 12/10/1997]
  If you cut a ruler with two arbitrary cuts, what is the probability of creating a triangle?

• Penny Toss [Kugelstadt, 12/17/1997]
  Three people each toss a penny at the same time. What is the probability that two people get the same side of the penny and the other person gets the opposite side?

• Pi and Probability [Leduc, 12/21/1997]
  I'm doing a report for my math class on the relation between pi and probability...

• Law of Random Numbers [Christie, 12/22/1997]
  I've recently been debating over the lottery...

• Probability Distribution [Smith, 12/22/1997]
  A county with a large number of rural homes is thought to have 60 percent of them insured against fire...

• Conditional Probability [Bonnette, 12/31/1997]
  I tutor probability and statistics and people seem to be confused by the use of the multiplication rule in conditional probability...

• Murder Rate Probability [Lankford, 01/12/1998]
  If a Midwestern town has a murder rate of 11 murders per year, what are the chances that 3 of them will occur on the same day?

• Lottery Probability [Meansaleen, 01/23/1998]
  Let's say that Monday's winning numbers were 1,2,3,4,5, and 6. Is the probability that those winning numbers will come up again the same?

• Roulette Questions [Castaneda, 01/26/1998]
  What is a safer bet: to bet on a number, or to bet on color? Which bet maximizes your wins: betting on numbers, or betting on colors?

• Coin Flipping [Lee, 01/26/1998]
  How can I figure out the chances of flipping a coin five times with the result T,T,T,H,H?

• Aircraft Disappearances [Ko, 01/29/1998]
  Seventy percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered...

• Toss a Coin Six Times [Beldon, 02/07/1998]
  Suppose a coin is tossed 6 times - what is the probability that 3 heads will occur...?

• Randomly Selecting a Card [Jordan, 02/20/1998]
  What is the probability that a card randomly selected from a standard deck will be a king and a club?

• AND and OR in Probability [King, 03/02/1998]
  Picking slips of paper from a hat, and comparison of AND and OR in probability.

• Probability of Matching Envelopes and Letters [Dey, 03/03/1998]
  Using inclusion-exclusion to calculate probability of matching no, then exactly one, letter with its envelope.

• Probability of Infection [Lictum, 03/06/1998]
  How many of six hermits can be expected, on average, to get a disease, assuming the disease is transmitted until an infectious hermit visits an immune hermit, and assuming one hermit visit per day?

• 5 cards are dealt from a perfectly shuffled deck [Chu, 03/16/1998]
  If you are dealt the ace of spaces, what is the probability of being dealt exactly 2 aces?

• Stochastic Matrices [Wayland, 03/17/1998]
  Finding the transtion matrix and steady-state vector of a stochastic process.

• Choosing Numbers with No Common Factors [Shen, 03/31/1998]
  What is the probability of choosing 2 numbers that have no common factors?

• Several Probability and Statistics Techniques [Evans, 04/13/1998]
  Examples of binomial distribution, Poisson distribution, significance test, and calculation of confidence interval.

• Drawing Marbles [West, 05/05/1998]
  A jar contains 19 different marbles. I draw 13 marbles, one at a time, but replace the marble back before taking the next....

• Probabilities and Expected Value in Seating Arrangements [Peters, 05/12/1998]
  Three couples are seated at random around a round table. Let M denote the number of husbands seated next to their wives ...

• Randomly Cutting a Rope into Two Segments [Luh, 05/14/1998]
  A rope 20m long is randomly cut into two segments, each of which is used to form the perimeter of a square . . .

• Prove Sum nci = 2^n ... [Andy, 05/30/1998]
  I would like to know how to prove sum nci = 2^n with 0<=i<=n.

• Probability and Pascal's Triangle [Ramirez, 06/04/1998]
  How do I find the probability of getting 3 head and 2 tails using Pascal's Triangle?

• Poisson and Binomial Questions [Hodgkinson, 06/13/1998]
  Can you explain why the waiting time in a Poisson process is exponential? Also, find the expected value of a binomial distribution?

• Moment Generating Functions [Hodgkinson, 06/20/1998]
  Can you help me with the following proofs on moment generating functions?

• Probability Theory: Coincidental Birthday [Ong, 06/21/1998]
  In more than half the classes in a school, there are at least two children with the same birth date...

• A Markov Chain Example [Hoschek, 07/01/1998]
  We are given P pots with N balls each and take B balls out of them, where B < N. On average, how many pots do we touch?

• Deriving the Normal From the Binomial [Chancellor, 07/11/1998]
  How is the normal distribution derived from the binomial distribution? Does the normal approximate the binomial?

• Standard Deviation and Conditional Probability [Williams, 07/14/1998]
  If a sample has one element, what is its standard deviation? Also, can you help me with a conditional probability problem?

• Probability Trees [Anderson, 07/26/1998]
  A bottle cap machine packs a defective cap in one box in ten. What is the probability the next four boxes will have a defective bottle cap?

• Monkeys Typing Shakespeare: Infinity Theory [Bridge, 08/05/1998]
  Would an infinite number of monkeys typing at random eventually produce the entire works of Shakespeare?

• Independent Events [DiCicco, 08/07/1998]
  Are the events A and B independent if P(A) = 0.6, P(B) = 0.2, and P(A and B) = 0.12?

• Markov Chains [Ramsay, 08/10/1998]
  Do you have an intuitive definition of a Markov Chain?

• Functions of Random Numbers [Reid, 08/26/1998]
  If you add or multiply a random number by a non-random number, do you still get a random number?

• Arranging Marbles in Boxes [Chris, 09/16/1998]
  Six marbles are placed in one of three different boxes. What is the probability that each box contains two marbles?

• Teaching Elementary Probability [Talmage, 10/07/1998]
  If you toss a number cube 20 times, could it land on six 20 times?

• Random and Pseudorandom Numbers [Sagebiel, 10/13/1998]
  When are the numbers of a sequence truly random numbers and not pseudorandom?

• Contest Probabilities [Zarinejad, 10/14/1998]
  Players of equal skill meet in an elimination contest. With n players, what is the probability that a player will compete in i rounds?

• Probability with the Poisson Distribution [Miller, 10/16/1998]
  Can you help me find a probability using a Poisson distribution? I need to be able to manipulate lambda.

• Banach Matchbox Problem [Akshay, 10/31/1998]
  Mr. Stephan kept two matchboxes, each with n matches. When he wanted a match, he chose the box at random. What is the probability that when he finds an empty box, the other will have k matches?

• Inclusive Probabilities [Africa, 11/06/1998]
  Can you explain the formula for inclusive probability: P(A or B) = P(A) + P(B) - P(A and B)?

• Poker, the Lottery [Mike, 11/08/1998]
  What is the probability that a 5-card poker hand will contain cards of 5 different values? To play the Pennsylvania superlottery, a player selects 7 of the first 80 positive integers...

• Game Theory and Payoff Matrices [Haldar, 11/14/1998]
  Can you give me a good introduction to game theory? What is a payoff matrix?

• Empirical and Mathematical Probabilities [Dettman, 12/04/1998]
  What is the difference between empirical probability and mathematical probability?

• Coin Tosses, Dealing Cards... [Greg, 12/08/1998]
  Several questions on discrete math - probability and combination; deducing recurrence relations.

• Stocks and the Binomial Distribution [Tom, 12/09/1998]
  If an index of stock prices has probability 0.65 of increasing in any year, how can you turn this into a binomial distribution question?

• Returning Homework and Probability [Bergman, 12/11/1998]
  When homework assignments are handed back at random, what is the probability that a student will receive his or her own paper?

• Server Traffic [Yaeli, 01/02/1999]
  Can you help me find a Poisson probabilistic model for number of arrivals per minute, length of connection, etc. ...?

• The Function g(x) = gcd(x, 10) [Mejia, 01/14/1999]
  Graph the function g(x) = gcd(x,10), where x is a positive integer. What is the range? Assign a probability that g(x) = r for each r in the range.

• Empirical Probability [Smith, 01/15/1999]
  If I flipped a coin 10 times and got heads each time, would the probability of a head on the next flip be 1/2 or almost 1?

• Randomly Setting the Table [Rooney, 01/25/1999]
  Using tree diagrams or incremental analysis to calculate the probability that, out of four differently colored and randomly placed settings, at least one setting (cup, saucer, and plate) is of the same color.

• Bayes Theorem [Brett, 02/06/1999]
  Could you please explain the mathematical difference between the following two situations... ?

• Probability Transition Matrices [Skor, 02/10/1999]
  How do you use probability transition matrices to find probabilities after the first transition?

• Poker Hand Probabilities [Burtin, 02/11/1999]
  What are the probabilities for all of the different types of poker hands?

• Biased Dice [Sharron, 02/18/1999]
  Assigning and adding probabilities.

• Poisson and Binomial Distributions [Jill, 02/22/1999]
  Some assumptions made in Poisson and Binary Distributions.

• Why Study Sequences and Series? [Tara, 02/26/1999]
  What are some applications of arithmetic sequences and series?

• Mean and Standard Deviation [Maria, 03/01/1999]
  Prove that the mean (u) and standard deviation (s) for a binomial distribution are np and the square root of (npq).

• At the Box Office [Michael, 03/08/1999]
  A "random walk" probability problem.

• Squares Having a Common Side [Suresh, 03/08/1999]
  What is the probability that two squares of a chessboard will have a common side?

• Randbin [Robert, 03/14/1999]
  Consider an airplane that has 113 seats... what is the probability that at most 113 will check in?

• Darts and Wilensky's Paradox [Morin, 03/17/1999]
  What is the probability of scoring 25 points with 2 darts if the dartboard is made up of 4 concentric circles?

• Explaining Bayes' Theorem [Battisfore, 03/22/1999]
  I need an easy-to-understand explanation of Bayes' Theorem to begin my math project for the math fair.

• Lifespan Probability [Dye, 03/26/1999]
  The probability that a general population will live past 85 is estimated to be 5.4 percent...

• Letters and Envelopes - the Inclusion-Exclusion Principle [Jarrad, 03/27/1999]
  What is the probability that no rabbit will escape into its own hole?

• Moment Generating Functions [Nandy, 03/30/1999]
  What can be established about the sum of negative binomial random variables?

• A Binomial Probability [Duncan, 04/10/1999]
  What is the Monte Carlo Method? If I roll a balanced die 100 times, what is the probability I will get 14-21 ones inclusive?

• Binomial Probability [Pacyon, 04/14/1999]
  A multiple-choice exam probability question.

• Sequence of Letters [Mellin, 04/23/1999]
  Given an alphabet of 10 letters and a sequence of 600 letters, what is the probability of finding the subsequence DDDD?

• Lost Town and Finder's Town: Bayesian Probability [Ming, 04/27/1999]
  A man is lost in the mountains... what's the probability that he's wandered into Lost Town? Finder's Town?

• Bertrand's Paradox [Krasik, 05/09/1999]
  What is Bertrand's Paradox?

• Rolling Dice [Laura, 05/16/1999]
  Find the probabilities of a total of 9 and a total of 10 when three fair dice are tossed once... Compare...

• Calculating Pi - the Nail Drop Experiment [Rob, 05/19/1999]
  Do you have any information about calculating pi by means of the nail drop experiment?

• Two Heads After N Tails [Wilson, 05/20/1999]
  What is the probability of flipping two heads after n number of tails?

• Bubbles in the Glass [Bushell, 05/22/1999]
  In a glass manufacturing process the probability of a glass having bubbles is 0.03...

• True/False and Multiple Choice Tests [Huxley, 05/24/1999]
  What is the probability of passing a 20-question true/false test by guessing?

• Tie Combinations [Feller, 05/31/1999]
  If four people have three identical ties, what is the total number of different combinations the four can wear, and what is the probability that all four people will wear the same tie?

• Let's Make a Deal Probability [McGinn, 06/01/1999]
  In "Let's Make a Deal," does Monty's showing you a door, or his knowing which door the prize is behind, affect the probability?

• Probability in Virus Testing [Warner, 06/04/1999]
  What is the probability that an individual who has a positive test result for the EB virus actually has the disease?

• Two Probability Questions [Prashant, 06/08/1999]
  What is the probability that all customers will get the type of butter they want? ...that every person who shows up for the flight will get a seat?

• Probability of Winning in Squash [Ashley, 06/23/1999]
  In a game of squash tied at 8 all, determine whether the player receiving the serve has a better chance of winning if she calls 9 or 10 points.

• Penny-moving Game [Kathy, 06/24/1999]
  If a penny is placed on the 3 on a number line and moved left or right based on the flip of a coin, what is the probability of it landing on 0 BEFORE it lands on 7?

• Consecutive Failures in Bernoulli Trials [Becker, 07/07/1999]
  What is the probability that out of n experiments there will be a string of at least k experiments in a row that fail?

• Guessing on True-False Tests [Darby, 07/08/1999]
  If you guess at each answer, are you more likely to answer at least half the questions right on a test with few or with many questions? Does it matter whether there is an even or an odd number of questions?

• A Truck and a Van [Pekkle, 07/11/1999]
  A small cartage company has two vehicles, a truck and a van... what proportion of the time is the van used?

• Poisson Distributions with Conditional Probability [Kathleen, 07/22/1999]
  Let X be Poisson(2), independent of Y which is Poisson(3); let W=X+Y. How can I find the distribution of X conditional on W=10?

• Hyper-geometric Distribution [Evette, 07/29/1999]
  Through a mix-up on a production line, 6 defective refrigerators were were shipped with 44 good ones...

• Predicting Divisional Winners [Jackie, 07/29/1999]
  A sportswriter "predicts" the winners of four divisions by choosing a team completely at random in each division. What is the probability that he will predict at least one winner correctly? What if he eliminates one also-ran? What if he draws four names out of a hat?

• Probabilities when Rolling 10 Dice [Jeffrey, 07/29/1999]
  What are the odds of a player rolling the same numbers in the same order as the house on 10 dice? ...of rolling the same numbers without regard to the order in which they were rolled?

• Sample Space Diagram [Anonymous, 07/30/1999]
  If a person randomly chosen from a population is found to be colorblind, what is the probability that the person is male?

• Hypergeometric Probability Distribution [Ernsdorff, 08/08/1999]
  Three consecutive bulbs are drawn without replacement at random from a box that contains 3 defective light bulbs and 7 good light bulbs. Construct a tree that shows all the possible outcomes?

• Probability of Forming a Triangle [Lawson, 08/09/1999]
  Three numbers are chosen (without picking the same number twice) from the first n natural numbers. What is the probability that they can be the three sides of a triangle?

• Definite Integral of e^(-x^2) and e^((-x^2)/2)) [Miller, 08/18/1999]
  How can I find the integrals of e^(-x^2) or e^((-x^2)/2)) from x = 0 to 1.96?

• The Birthday Problem; Queueing at a Bank [Carreker, 08/26/1999]
  If each of 40 customers at a bank chooses 1 of 5 tellers at random, what is the probability that teller number 2 will have no customers?

• Tips on Solving Probability Problems [Tsang, 08/27/1999]
  Questions about probability distribution involving means, standard deviations, Poisson distributions, independent random variables and conditional probability.

• Three Share a Birthday [McGraw, 09/17/1999]
  What is the probability that in a class of 24 students, 3 of them will share the same birthday?

• Multiple Regression vs. ANOVA [Voorhis, 09/20/1999]
  What is the difference between multiple regression and ANOVA (ANalysis Of VAriance) procedures?

• Moment-generating Function of a Binomial Random Variable [Lockett, 10/27/1999]
  How can I find the moment-generating function (MGF) of a binomial random variable?

• Most Frequently Rolled Number [Nesbitt, 10/27/1999]
  What sum would be rolled most often if two dice, each numbered -3, -2, -1, 0, 1 and 2, were rolled 100 times?

• The Probable Pen in the Cereal Box [Kuropatwa, 11/25/1999]
  Six different-colored pens are offered as prizes in boxes of breakfast cereal. How many boxes of cereal do you have to buy to get all six?

• Four of a Kind in Half a Deck of Cards [Kevin, 11/26/1999]
  If a full deck of cards is cut in half, what are the chances that at least one type of a card (i.e. Kings, Aces) will have all four suits present?

• Boy or Girl: Two Interpretations [Reid, 01/03/2000]
  How can the probability be 2/3 of a boy in a two-child family having a sister? Shouldn't it be 1/2?

• Probability in a Dice Game [Leona, 01/04/2000]
  How can I find the probability of each player winning, and the most likely length of the game, for a dice game that may continue forever?

• Ten Ducks and Ten Hunters [Amal, 02/03/2000]
  Ten ducks fly overhead. Each of ten hunters picks one duck at random to aim at and kill it with probability P. What is the mean number of ducks killed?

• Collecting a Set of Coupons [Amal, 02/03/2000]
  Given N different types of coupons, what is the expected number of different types of coupons that are contained in a set of (n) coupons? What is the variance and the expected number of coupons one one needs to collect before obtaining a complete set?

• Satellites and Dartboards [Borden, 02/21/2000]
  If I know the surface area and number of satellites in orbit, and the divergence of a laser beam fired from a random point on earth, how can I determine the probability of hitting one of the satellites?

• Collecting a Complete Set [Butler, 03/15/2000]
  I have a very large box filled with 8 different frying pan handles in equal proportions. What is the probability that I will have to remove 32 handles before I get a complete set?

• Predicting NCAA Tournament Winners [Pleasants, 03/27/2000]
  What are the odds of one person predicting the winners of all 63 games in the NCAA Basketball Tournament?

• Past Events and Probability [Peter, 04/05/2000]
  Do the results of past events affect future outcomes in probability? If they don't, why is it more likely that you will get 8 heads in 10 coin tosses than 10 heads in those 10 tosses?

• Probability and the game of RISK [Peretti, 04/21/2000]
  In the game of Risk the attacker rolls 3 dice, the defender rolls 2 dice and high dice are compared...

• Lottery Strategy and Odds of Winning [Smith, 04/27/2000]
  Are my odds of winning the lottery the same whether I choose the same numbers each time or whether I choose different numbers?

• Phone Number Combinations [Moussa, 05/07/2000]
  Linda knows the first 3 digits of Jack's phone number, but she doesn't know the other 4...

• Expected Value of Area of Triangle [Jones, 05/10/2000]
  What is the expected value of the area of triangle APB if AB is the diameter of a circle with radius r, AP is a chord, and X is the angle between AB and AP, uniformly distributed over the interval 0 to pi/2?

• Probability of a Function Having Complex Roots [Henrik, 05/11/2000]
  What is the probability that the function f(x) = x^2 + px + q = 0 will have complex roots when p and q lie between 0 and 1? ...when p and q lie between 0 and 5? ...when p and q are greater than 0?

• Finding a Steady-State Probability Matrix [Hitch, 05/12/2000]
  Find the steady-state matrix for the likelihood of a guard's being at each of the corners of a rectangular lot, if he is instructed to wait 10 minutes at each corner, and then either stay where he is or move to one of the adjacent corners randomly.

• Making a Conditional Probability Chart [Dolan, 05/17/2000]
  In a group of patients screened for lung cancer, 10% have the disease. Of those who have lung cancer, 93% are smokers. Of those who do not have lung cancer, 28% are smokers. If a person selected from this group is a smoker, what is the probability that the person has lung cancer?

• Getting Two Heads in Four Tosses of a Coin [Melissa, 05/17/2000]
  What is the probability of getting two heads on four flips of an unbiased coin?

• Conditional Probability [Sultan, 05/25/2000]
  Suppose used car salesmen tell the truth 2/5 of the time, and 1/3 of the trees in a forest are oak...

• A Triangle in a Circle [Gamache, 05/26/2000]
  Suppose you randomly place 2 points on the circumference of a circle. What is the probability that a 3rd point placed randomly on the circle's circumference will form a triangle that will contain the center of the circle?

• Finding My Car Key on the Second Try [Stubbs, 05/29/2000]
  There are seven car keys in a box, including mine. I'm going to randomly remove one key at a time, and then try to start my car...

• Getting More Heads [Ruiz, 05/29/2000]
  If Bob flips 850 fair coins and Alice flips 851 fair coins, what is the probability that Alice will get more heads than Bob?

• Calculating a Casino's Edge From Odds [Sheridan, 05/30/2000]
  How can I calculate the casino's edge, if the odds of winning are 5 to 1 and the casino's payout is 4 to 1?

• Winning the Game [Lane, 09/21/2000]
  In an equitable game of coin tossing, I have x dollars and my friend has y dollars... What is the probability that my friend will win all of my x dollars before I can win his y dollars?

• Years That Start on Sunday [Lane, 10/02/2000]
  What is the probability that a randomly chosen year will start on a Sunday?

• Math in Card Games [Joshi-Powell, 10/06/2000]
  How is math involved in creating and playing card games?

• The World Series [Erin, 10/22/2000]
  What is the probability of the Yankees and the Mets playing each other in the World Series?

• Card Game Analogous to Monty Hall? [Lozano, 12/12/2000]
  I think I have an analogy to the Monty Hall problem that proves that your chances are 1/2 if you switch, not 2/3...

• Die Roll Probabilities in Gaming [Ferrell, 01/06/2001]
  Players fight battles by rolling two dice and adding modifiers according to each player's advantages. Generate a chart giving the odds of victory based on modifiers.

• Fair Value of a Coin Toss Game [Shah, 01/21/2001]
  Suppose you play a game where you toss a coin until tails turn up...

• Choosing a Random Rational Number [Platt, 01/23/2001]
  0 percent probability should mean that it is impossible for a rational number to be chosen from the set of real numbers, but obviously this isn't the case. How can it be 0 percent probability but not impossible?

• Odds and Probability (A Heated Argument) [Mike, 01/24/2001]
  My friend and I are having a raffle. It has 40 prizes in it...

• Proving Conditional Probabilities [Walker, 01/24/2001]
  If P(B|A) is greater than P(B), prove that P(B^c|A) is less than P(B^c).

• Probability of Forming a Triangle [Mike, 01/24/2001]
  A rope one unit long is cut in two places. What is the probability that the three resulting pieces can be arranged to form a triangle?

• Three Heads in a Row [Curtis, 01/25/2001]
  How many flips of a coin on the average will it take to get three heads (or tails) in a row?

• Running Shoes [Detti, 02/07/2001]
  What proportion of the time does the runner run barefoot?

• Stock Market Scam [Gray, 02/08/2001]
  Every Monday a firm sends you a letter correctly predicting the behavior of a given stock over the coming week. In the 8th letter the firm offers to sell you more predictions for a fee. You refuse. Why?

• The Law of Large Numbers [Rothstein, 02/08/2001]
  Can you give me a brief explanation of the law of large numbers?

• Most Desirable Properties in Monopoly [Price, 02/16/2001]
  What are the most desirable properties on a Monopoly board? How can we calculate the overall probability of landing on a given property?

• Monty Hall Logic [Dinwiddie, 03/09/2001]
  Are there in fact four options? Aren't there three choice points, not just two?

• Four of a Kind in a 13-Card Hand [Tran, 03/24/2001]
  What is the probability of receiving four-of-a-kind when dealt 13 cards from a regular 52-card deck?

• Twist on Monty Hall [Rick, 03/31/2001]
  You can open as many of the doors as you like, but you have to stay with the last door that you open...

• Probability of Never Having a Losing Record [Bulut, 04/07/2001]
  Suppose a football team plays 8 games, and the chance of winning any particular game is 50%. What is the probability of completing the season without more losses than wins?

• Probability Axioms and Theorems [George, 04/10/2001]
  What are the laws of probability?

• Sharing a Zodiac Sign [Katrin, 04/24/2001]
  In a class of 35 students, what is the probability that every student in the class will have the same zodiac sign as at least one other classmate?

• Distribution of Cards in Bridge [David, 05/03/2001]
  In bridge, it often happens that you and your partner have 9 cards of a suit between you. In all the bridge books that I have read, it is stated that the probability of the remaining 4 cards splitting 2-2 is 40.7%. Can this be proven?

• Theoretical and Experimental Probability [Laura, 05/07/2001]
  If we spin a spinner 20 times and record the results, what might we conclude from our experiment?

• Law of Large Numbers and the Gambler's Fallacy [Basilio, 05/07/2001]
  Should you get the same total, on average, when you make three throws of three dice each as when you throw nine dice at once? Also, can you explain the Law of Large Numbers and the Gambler's Fallacy?

• Probability of Choosing a Face Card [Timi, 05/08/2001]
  If you pick a card from a regular deck of cards (52), what is the probability of getting a face card three times in a row?

• Batting Averages [Robb, 05/08/2001]
  I have a question concerning the Law of Large Numbers and the Gambler's Fallacy as related to baseball player batting averages.

• Ten Coin Flips, Four Heads [Timi, 05/08/2001]
  If you flip a coin ten times, what is the probability of getting at least four heads?

• Coin-Tossing Game [Ashutosh, 05/09/2001]
  Three men toss a coin in succession for a prize to be given to the person who first obtains a head. What is each man's chance of winning the prize?

• Colored and Numbered Discs [Morley, 05/25/2001]
  Drawing colored and numbered discs from boxes; rolling colored and numbered dice.

• Getting One of Each Number (1-6) Rolling N Dice [Kevin, 05/24/2001]
  I've been trying to determine various probabilities involving randomly distributing items to a group of six people...

• Rolling a Die 600 and 5000 Times [Tory, 06/03/2001]
  Toss a die 600 times, 5000 times. How many times does each number come up? Approximately how many would you expect?

• Working Out Betting Odds [Phil, 06/27/2001]
  I am doing a horse racing night in a local pub, and as part of the committee I have been asked to try to find out how to work out the betting odds for each horse...

• Probability and the Prisoner Problem [Nick, 07/04/2001]
  Each of 16 prisoners receives a hat that is either red or blue (the colour is selected randomly; each has a 1/2 probability). All the prisoners must simultaneously either try to guess the colour of their hats, or pass.

• Odds of Winning the PowerBall Lottery [Joseph, 08/29/2001]
  Was the article that stated that the odds of winning the 300-million- dollar powerball were just one in 80,089,128 correct?

• Probability C Hits the Target First [Rob, 09/08/2001]
  A, B, and C keep shooting in the sequence: A,B,C,A,B,C... until a target is hit. A hits the target 5/6 of the time, B 3/4 of the time, and C 2/3 of the time. What's the probability that C will hit the target first?

• Closed Envelopes Paradox [Dror, 09/13/2001]
  You must choose between two closed envelopes, one with a certain amount of money and the other with twice as much...

• Probability Interior Angles are Positive Integers [Guili, 09/19/2001]
  Find the probability that the measure of an interior angle of a regular n-gon is a positive integer if n is an integer and 3
• Lung Cancer and Smoking [Nin, 10/20/2001]
  Medical researchers know that the probability of getting lung cancer if a person smokes is .34. The probability that a nonsmoker will get lung cancer is .03. If 11% of the population smokes, what is the probability that a person with lung cancer will have been a smoker?

• Expected Value [Hermann, 11/07/2001]
  I am playing a game where I toss a fair coin. I get a bead if I flip a head and I lose a bead if I flip a tail... to get a total of 5 beads, what is the expected number of coin tosses I must make?

• The N Targets Problem [Jocelyn, 11/15/2001]
  Given n targets with equal probability of being hit by a cannon, that is, 1/n. Let X be the number of firings required to hit all the targets. What is the expectation E(X) of X?

• Coin Landing on Edge [Robert, 11/20/2001]
  Is there a way to calculate the odds of a coin dropped from a known height landing on its edge rather than heads or tails?

• Coin Landing on Edge [Milner, 11/29/2001]
  What are the chances of a coin landing on edge? A Canadian copper penny, round.

• Choosing Chocolate Bars [Tracie, 12/04/2001]
  If I have 3 Mr. Goodbars, 13 Hershey milk chocolate bars, 7 Special Dark bars, and 3 Krackel bars, what is the probability that I will get at least 1 Krackel if I pull two out of the bag at the same time?

• Sum of Two Dice [Emily, 12/05/2001]
  Find the probabilities of rolling different sums.

• Bit Strings with Even Numbers; Coin Toss [Erin, 12/09/2001]
  How many bit strings of length n have an even number of 1's? A fair coin is tossed until 2 consecutive heads appear. What's the probability that this will happen within the first n tosses?

• Binomial Distribution [Lisa, 12/13/2001]
  37% of people over age 80 will not be around within the next 10 years. In a random sample of 113 senior citizens, find the probability that in the next 10 years, at most 90 will die.

• English Exam Probability [Hunter, 12/17/2001]
  Given a list of 25 potential exam questions, with 10 of them on the actual exam and of which students write essays on 2, how many questions should be prepared to be 95% confident you won't write on a question you haven't prepared?

• Rolling 3 Pairs with 6 Dice [Jeremy, 12/19/2001]
  Upon playing the game '10,000' on the computer I was struck by the frequency with which 3 pairs came up...

• Powerball Odds When Buying More Tickets [Daren, 12/31/2001]
  If the odds are 80,000,000 to 1 of buying a winning ticket, do they go to 40,000,000 to 1 if you buy 2 tickets?

• Cupcakes and Boxes: Conditional Probability [Snowball, 01/03/2002]
  Given 3 boxes, each with 2 cupcakes (1 box has two vanilla, 1 has 2 chocolate, and 1 has one of each). A box is selected randomly and a cupcake is selected that turns out to be chocolate. What's the probability that the other cupcake in that box will be chocolate?

• Choosing Scrabble Letters [Matthew, 01/07/2002]
  In a Scrabble game with two players, each must randomly choose seven letters. Does it matter whether each player chooses all seven letters at once or they alternate back and forth, taking one at a time?

• Independent, Uniformly Distributed Random Variables [Damian, 01/10/2002]
  Given two independent, uniformly distributed random variables X and Y in {0,1,...,n}, calculate the probability of (X=j I X+Y=k)...

• Infinite Series Problem [Flori, 01/15/2002]
  I have to find the correct answer to an infinite series question about three people throwing dice...

• Combinatorial Probability Tournament [Penina, 01/23/2002]
  A tennis tournament for 2^n players is organised as a knock-out tournament with n rounds, the last round being the final. Two players are chosen at random. Calculate the probabilities they meet a) in the first round; b) in the final; c) in any round.

• M Balls in N Boxes [Tanya, 01/24/2002]
  Suppose we put m balls into n boxes. What is the expected number of empty boxes?

• Find the Density Function [Tanya, 01/24/2002]
  Suppose X1, X2, X3 are independent and uniform on(0,1). Find the density function of S = X1 + X2 + X3.

• Online Lottery [Ashok, 02/01/2002]
  What is the chance of matching the numbers? How is it calculated?

• Greatest Probability Neither Event Will Happen [Lucia, 02/02/2002]
  The probability that event A will happen is 0.54, and the probability that event B will happen is 0.68; what is the greatest probability that neither of the events will happen?

• Even Number of Heads [Courtney, 02/12/2002]
  What is the probability of getting an even number of heads when tossing a biased coin?

• Horse Racing Odds [Kevin, 02/21/2002]
  In horse racing the odds often add up to more than one. Why?

• Space Diagrams [Stephen, 02/28/2002]
  A bag contains 3 blue balls, 1 red ball and 1 white ball. A second bag contains 1 blue ball and 4 red balls. A ball is chosen at random from each bag. Draw a sample space diagram to show the possible outcomes.

• What is a Biased Die? [Rehan, 03/01/2002]
  How do we find the probability when the dice are biased?

• Central Limit Theorem [Stephanie, 03/08/2002]
  The probability that a drug is effective in any one patient is 62%. Find the probability that, of the next 200 patients, at least half (or more) will survive.

• Probability in Yahtzee [Julie, 03/20/2002]
  What is the probability of rolling two of a kind three times? four of a kind? all five the same on the first roll? again on the second?

• Three People Toss a Coin [George, 03/22/2002]
  Three people each toss a coin in order. The winner is the first to get a 'tail'. Expressed as fractions, what are their respective chances of winning?

• Probability vs. Odds, Explained [Brett, 03/21/2002]
  Given a coin with heads on one side and tails on the other, what are the odds in favor of getting heads, and the odds against?

• What If You Paint the Balls? [John, 03/25/2002]
  Given 800 blue balls in a bag, you take out 35 of them, paint them red, and replace them. Do this 23 times and you *might* paint all of them - what are the odds?

• Rolling One Die Twice [Zack, 03/25/2002]
  If one die is rolled twice, what is the probability of getting a 10?

• Johnny Carson's Birthday Problem [Murad, 04/03/2002]
  Carson picked people at random. Why didn't the probability work out?