Green Book Chapter 4

All problems from the Green Book ch4.

Two gamblers are playing a coin toss game. Gambler A has (n+1) fair coins; B has n fair coins. What is the probability that A will have more heads than B if both flip all their coins?

0.5

A casino offers a simple card game. There are 52 cards in a deck with 4 cards for each value 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A. Each time the cards are thoroughly shuffled (so each card has equal probability of being selected). You pick up a card from the deck and the dealer picks another one without replacement. If you have a larger number, you win; if the numbers are equal or yours is smaller, the house wins-as in all other casinos,the house always has better odds of winning. What is your probability of winning?

A line of 100 airline passengers are waiting to board a plane. They each hold a ticket to one of the 100 seats on that flight. For convenience, let's say that the n-th passenger in line has a ticket for the seat number n. Being drunk, the first person in line picks a random seat (equally likely for each seat). All of the other passengers are sober, and will go to their proper seats unless it is already occupied; In that case, they will randomly choose a free seat. You're person number 100. What is the probability that you end up in your seat (i.e., seat #100) ?

Given N points drawn randomly on the circumference of a circle, what is the probability that they are all within a semicircle?