Alice believes that the 49ers will win the Super Bowl with probability 5/8. Bob believes that Ravens will win the...
Continue reading...probability
Medical Tests and Bayes’ Theorem
Suppose that you are worried that you might have a rare disease. You decide to get tested, and suppose that...
Continue reading...St. Petersburg Paradox
A new casino offers the following game: you toss a coin until it comes up heads. If the first heads...
Continue reading...Farmers and Pesky Birds
Alice and Bob are two farmers each wanting to plant a (countably infinite) row of seeds, side by side in...
Continue reading...Volume of a Ball in N Dimensions
The unit ball in Rn is defined as the set of points (x1,…,xn) such that x12 + … + xn2 <= 1. What...
Continue reading...Poker Probability Paradox
In poker, there is a hierarchy of desirable hands which relate to how unlikely the hand is. For instance, a...
Continue reading...Monty Hall Problem
Here’s a problem that makes the round every few years, and each time, it is hotly debated. You are on...
Continue reading...Deal or No Deal
On the TV show “Deal or No Deal”, a contestant is faced with a number of briefcases (26 in the...
Continue reading...Seven Shuffles
How many shuffles does it take to randomize a deck of cards? The answer, of course, depends on what kind...
Continue reading...Pass the Beer
Suppose you and a bunch of friends are sitting around a table. There are N of you. You have a...
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