Birthday boy.

Imagine you're sitting in a room with 22 other people in it, what are the chances that two amongst you have the same birthday? For simplicity's sake, you can ignore leap years.

Hints and solutions

The last passenger.

Q. On a sold out flight, 100 people line up to board the plane. The first passenger in the line has lost his boarding pass, but was allowed in, regardless. He takes a random seat. Each subsequent passenger takes his or her assigned seat if available, or a random unoccupied seat, otherwise. What is the probability that the last passenger to board the plane finds his seat unoccupied?

Solution