St. Patrick’s Day

The Google Doodle of the day tells me that it’s St. Patrick’s Day today, so what better way to celebrate than with some math problems?

1) A leprechaun is playing a game. He rolls a die, and every time his roll and the number opposite on the (normal, six-sided) die sum to seven, he drinks a quart of beer. After four rolls, what is the probability that the leprechaun has drunk a gallon of beer?

2) At the leprechaun bar, the probability that a leprechaun is forbidden another drink by the bartender is the same as the probability of flipping an infinite number of tails in a row with a fair coin. How many leprechauns go home sober?

3) Two leprechauns are playing ping pong with a ball with a coefficient of restitution of 0. The loser of each point drinks a pint of beer. What is the final score of the game, how long does the game take, and how drunk are the leprechauns at the end of the game?

Answers to come in my next post, and for the record, here’s the real reason St. Patrick’s Day is celebrated.