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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.

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?

Banana Stickers [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?

Batting Averages [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.

Bayesians and Frequentists [08/21/2001]
What is the difference between Bayesian and "regular" statistics?

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

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

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

Binomial and Geometric Probability Distributions [10/20/2005]
What is the probability of rolling exactly one 6 in n rolls of a die?

Binomial Distribution [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.

Binomial Distribution [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.

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

Binomial Experiments [09/05/2003]
How can I explain the binomial distribution to my six grade math class?

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

A Binomial Probability [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 Formula [03/22/2005]
Sue makes 70% of the free throws she attempts. She shoots three free throws in her warmup before a game. What is the probability that Sue makes two or more of the three free throws?

Birthday Probabilities [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?

The Birthday Problem; Queueing at a Bank [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?

Bit Strings with Even Numbers; Coin Toss [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?

Blackjack [10/01/2003]
Given a standard deck of cards, what is the probability of getting blackjack on the first two cards drawn?

Boy or Girl: Two Interpretations [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?

Boy, What Is Your Probability? [12/18/2016]
A teen struggles to make sense of a variation of the girl-or-boy puzzle. After some re-wording, Doctor Vogler steps through the branches of the probability tree.

Break a dowel to form a triangle [3/8/1995]
A wooden dowel is randomly broken in 2 places. What is the probability that the 3 resulting fragments can be used to form the sides of a triangle?

Bridge Hand Probability [12/02/2008]
While playing Bridge, your hand has 9 cards in two suits (5 in one and 4 in the other). What is the probability of your partner having 4 cards in one of your two suits?

Bubble Gum Cards [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...

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

Calculating a Casino's Edge From Odds [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?

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

Card Game Analogous to Monty Hall? [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...

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

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

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

Central Limit Theorem [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.

Chances of Winning a Raffle [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?

Checkerboard Chase [12/13/2002]
Player A begins by placing a checker in the lower left-hand corner of a checkerboard (8 by 8 squares). Player B places a checker one square to the right or one square up or one square diagonally up and to the right of Player A's checker... Would you rather be Player A or Player B?

Checking Account Balance [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?

Chocolate Chip Probability Word Problem [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?

Choosing a Random Rational Number [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?

Choosing Chocolate Bars [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?

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

Choosing Scrabble Letters [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?

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