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Browse High School Probability
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Coin tossing.
    Odds vs. probability.
    Poker probabilities.
    Rolling dice.

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

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

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

Raffle Reckonings [09/22/2017]
In a raffle that promises 1-in-30 winning odds, an adult wonders how her much her luck increases if she buys 45 tickets. Introducing factorial notation, Doctor Ian sets up a simpler version of her question, models how to calculate the chance of winning — and reveals why her erroneous method approximated the correct probability.

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

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

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

Random Card Shuffling Probabilities [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?

Randomly Cutting a Rope into Two Segments [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 . . .

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

Randomly Setting the Table [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.

Reliability of Independent Batteries [02/08/2012]
A satellite runs on battery, with a second, separate cell backing it up. With what likelihood will it outlast the expected service life of one of the batteries? How do you compute the satellite's expected lifetime? Doctor Anthony applies the formulas for two parallel probabilities and expectations.

Returning Homework and Probability [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?

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

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

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

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

Roulette Betting "System" [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...

Roulette Probability [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?

Roulette Questions [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?

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

Sample Space Diagram [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?

Satellites and Dartboards [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?

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

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

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

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

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

Sharing a Zodiac Sign [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?

Should You Play? [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?

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

Simplifying a Probability Question [08/19/2008]
An example of how a probability question that seems difficult or confusing can often be simplified by translating it into an equivalent situation involving colored balls in a jar.

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

Social Security Number Probability [02/09/2004]
What are the chances that a 9-digit Social Security number is comprised entirely of 2 digits, such as 211-12-1221?

Space Diagrams [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.

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

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

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

Stock Market Scam [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?

Stocks and the Binomial Distribution [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?

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