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Dr. Math FAQ:
probability in the
Browse High School Probability
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Selected answers to common questions:
Odds vs. probability.
- Conditional Probability [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 [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 [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 [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?
- Gambler's Fallacy [03/14/2003]
My co-worker prefers to bet the same set of five lottery numbers every time, but I say that the probability is the same if you randomly select any set five numbers for the same period of time. Who is right?
- Geodesics [12/15/1996]
Can you give me information on the math behind geodesics?
- Independent and Dependent Events [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 [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
- Math Symbol for C [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 [11/27/2001]
Montana duck hunters are 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
- Odds Slang for Probability? [02/06/1997]
Is "odds" slang for probability?
- Odds vs. Probability [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?
- One Person of Seven Born on Monday [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 [08/07/1997]
What are the odds of getting exactly one pair in five card stud poker,
using one 52-card deck?
- Powerball Lottery: Odds of Winning a Prize [09/02/2001]
How are the Powerball lottery odds established?
- Probabilidad de que Juan y María se encuentren [6/27/1996]
Juan y María quedan a encontrarse entre las 7:00 y 8:00 en un
- Probability and Genetics - Huntington's Disease [12/30/2001]
I am doing a math paper on Huntington's Disease. What does probability
have to do with genetics?
- Probability: Let's Make a Deal [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 Being Born on Monday [8/26/1996]
What is the probability that of any seven persons exactly one was born on
- Probability of Hitting Safely [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 Rolling a 6 on One Die [4/30/1995]
The following questions came up during a game of Risk...
- Probability of Two Dice Summing to 5 [09/22/2001]
If a person rolls two dice, what is the probability of getting a five as
- Probability of Two Male Children [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 [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? [10/30/2001]
When do you add and when do you multiply to compute probability?
- Why Add Probabilities in an OR Statement? [05/25/1999]
Why when we want to find the probability of, for example, rolling a 2 or 3 on a die, do we add the number of twos and threes?
- 2-Digit Number is Multiple of 14 [9/10/1996]
What is the probability that a randomly selected two-digit number is a
multiple of 14?
- 30 hat probability question [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...
- 5 cards are dealt from a perfectly shuffled deck [03/16/1998]
If you are dealt the ace of spaces, what is the probability of being
dealt exactly 2 aces?
- An Absorbing States Problem [11/28/2000]
A mouse is in one of 4 rooms. If it finds cheese in the current room, it
stays there; if not, it exits to another room at random. What is the
probability it will get trapped? Are there any absorbing states?
- Advanced Probability as Used in a MAGIC [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.
- Aircraft Disappearances [01/29/1998]
Seventy percent of the light aircraft that disappear while in flight in a
certain country are subsequently discovered...
- AND and OR in Probability [03/02/1998]
Picking slips of paper from a hat, and comparison of AND and OR in
- Are They Wearing Seatbelts? [3/26/1995]
80 percent of all California drivers wear seatbelts. If 4 drivers are
pulled over, what is the probability that all 4 will be wearing their
- Arranging Marbles in Boxes [09/16/1998]
Six marbles are placed in one of three different boxes. What is the
probability that each box contains two marbles?
- Assigning Committees using Probability [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?
- At the Box Office [03/08/1999]
A "random walk" probability problem.
- Average Time for a Mouse to Find Cheese [11/05/1997]
A mouse has three rooms to go into...
- Baccarat; a Casino Game [5/22/1996]
Information on the probabilities of baccarat.
- Banach Matchbox Problem [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?