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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
- 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
- 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
- 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
- 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 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
- 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?