Probability Puzzle 1: The Birthday Problem There are 23 people in this class. What is the probability that at least 2 of the people in the class share the same birthday? Probability Puzzle 2: The Game Show Paradox Let's say you are a contestant on a game show. The host of the show presents you with a choice of three doors, which we will call doors 1, 2, and 3. You do not know what is behind each door, but you do know that behind two of the doors are beat up 1987 Hyundai Excels, and behind one of the doors is a brand new Cadillac Escalade. The cars were placed randomly behind the doors before the show, and the host knows which car is where. The way the game is played out is as follows. The host lets you choose a door. Assume you choose door #1. Before he opens door #1 to let you see what you have chosen, he opens one of the remaining doors, say door #3, to reveal a Hyundai Excel (he will always open one of the remaining doors that has the booby prize), and asks you whether or not you want to change your choice to door #2. What do you tell him? Probability Puzzle 3: Flipping Coins If you flip a coin 3 times, the probability of getting the sequence HTH is identical to the probability of getting HTT (1/8). Let's make this situation a little more interesting. Suppose you are going to flip a coin until you get the sequence HTH. Say this takes you x flips. Then, suppose you are going to flip the coin until you get the sequence HTT. Say this takes you z flips. On average, how will x compare to z? Will it be bigger, smaller, or equal? Probability Puzzle 4: Disease Testing and False Positives Assume that the test for some disease is 99% accurate. If somebody tests positive for that disease, is there a 99% chance that they have the disease? Probability Puzzle 5: A girl named Florida Here's a three part puzzler: 1. Your friend has two children. What is the probability that both are girls? 2. Your friend has two children. You know for a fact that at least one of them is a girl. What is the probability that the other one is a girl? 3. Your friend has two children. One is a girl named Florida. What is the probability that the other child is a girl