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

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 times?

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 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.

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?

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

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?

Bell Numbers Formula [02/13/2001]
How is the formula for Bell numbers derived from the Stirling numbers formula?

Betting Strategy [05/02/2003]
Suppose 2 teams play a series of up to 7 games in which the first team to win 4 games wins the series, and then no more games are played...

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?

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?

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?

Calculating a Probability Density Function from a Moment Generating Function [04/04/2009]
Given M_y(t) = (1/(1 - t))^2, compute P(-2 < Y < 3) -- or explain why it cannot be computed.

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?

Chocolate Chips per Cookie and Poisson Probabilities [06/12/2004]
A bakery makes a batch of 200 cookies in which 2000 chocolate chips were used. What is the probability that a cookie picked at random from the batch will contain at least 13 chocolate chips?

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

Coin Flipping: Confusing Mean and Median [01/31/2003]
Why is there a difference between the probability of four heads in a row in twenty coin tosses, and the number of tosses needed for a 50% chance of four heads in a row?

Coin Landing on Edge [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 Toss Probability [05/26/2007]
If a coin is tossed 100 times, what is the probability that you get less than or equal to 40 heads?

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

Combined Probability of Unrelated Events [7/23/1996]
Five cards are drawn without replacement from each of three standard decks of playing cards... what is the probability that the ace of spades will appear once?

Compound Probabilities [6/28/1996]
A linear combination of random numbers with uniform probability density within a certain range, say zero to one...

Conditional Probability [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...

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

Craps and Betting Systems [03/17/2003]
In craps, can I bet on the 7 and win (more than I lose) if I assume a seven normally comes up within 32 rolls?

Creating a Mathematical Model of a Complicated Situation [10/09/2005]
I am riding a bike and have several possible routes, each of which contains various traffic lights, amounts of traffic, the possibility of being stopped by a policeman for running a light, and other factors which influence the time it will take to ride each route. How can I model the routes to predict which will be the best choice?

Defining Independent Events [07/14/2009]
My book says two events E and F are independent if P(E|F) = P(E). Do we also have to have P(F|E) = P(F) or does this automatically follow? Could there be a situation where P(E|F) = P(E) but P(F|E) =/= P(F)?

Distinguishing between Two Random Sequences [05/09/2008]
Is there any efficient way, such as a polynomial-time algorithm in L, to distinguish between a distribution which takes L elements at random in [1, N] and one which takes L elements at random in [1, N], then picks a random v in [1, L] and replaces x_v with a random element in [1, N/2]?

Distribution of Cards in Bridge [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?

Do Prior Outcomes Affect Probabilities of Future Ones? [05/26/2008]
I know that the probability of flipping a coin and getting a head is 1/2. But if I've gotten ten straight tails, isn't it more likely that the next one will be a head?

Expected lifetime in an Exponential Distribution [10/28/1999]
The lifetime X of an electronic component has an exponential distribution such that P(X less than or equal to 1000) = 0.75. What is the expected lifetime of the component?

Expected Number of Plays to End the Game [06/19/2009]
Bob and Kyle each have $18. They flip a fair coin repeatedly. If the coin comes up tails, Bob pays Kyle $1. If the coin comes up heads, Kyle pays Bob $1. The game is finished when either one of them has no money left. What is the expected number of coin flips this game will last?

Expected Value of Area of Triangle [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?

Finding a Steady-State Probability Matrix [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.

Finding My Car Key on the Second Try [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...

Finishing a Best-of-Seven Series [06/19/2009]
A best-of-seven series is currently 2 games to 1 in favor of team A. If the two teams are equally likely to win a given game, what is the probability that A wins the series by reaching 4 games before B does?

Five-Card Straight [12/10/2002]
From a standard 52-card deck you pull out a 5-6-7-8 (suit is irrelevent). You shuffle the remaining 48 cards and deal 3 more. What percentage of the time will you complete the 5-card straight?

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