# probability

## Risk-Free Betting on Different Beliefs

Alice believes that the 49ers will win the Super Bowl with probability 5/8. Bob believes that Ravens will win the...

## 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...

A new casino offers the following game: you toss a coin until it comes up heads. If the first heads...

## Farmers and Pesky Birds

Alice and Bob are two farmers each wanting to plant a (countably infinite) row of seeds, side by side in...

## 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...

In poker, there is a hierarchy of desirable hands which relate to how unlikely the hand is. For instance, a...

## Monty Hall Problem

Here’s a problem that makes the round every few years, and each time, it is hotly debated. You are on...

## Deal or No Deal

On the TV show “Deal or No Deal”, a contestant is faced with a number of briefcases (26 in the...