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Browse College Probability
Stars indicate particularly interesting answers or
good places to begin browsing.
See also College Statistics.
 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 twochild 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 lefthand 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(EF) = P(E). Do
we also have to have P(FE) = P(F) or does this automatically follow?
Could there be a situation where P(EF) = P(E) but P(FE) =/= P(F)?
 Distinguishing between Two Random Sequences [05/09/2008]

Is there any efficient way, such as a polynomialtime 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 22 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 SteadyState Probability Matrix [05/12/2000]

Find the steadystate 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 BestofSeven Series [06/19/2009]

A bestofseven 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?
 FiveCard Straight [12/10/2002]

From a standard 52card deck you pull out a 5678 (suit is
irrelevent). You shuffle the remaining 48 cards and deal 3 more. What
percentage of the time will you complete the 5card straight?
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