QuoraUpdateCancelAnswer WikiAnswered 215w ago · Author has 175 answers and 394k answer views1. MONTY HALL PROBLEM- Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats.
1, and the host, who knows what's behind the doors, opens another door, say No.
He then says to you, "Do you want to pick door No.
2?" Is it to your advantage to switch your choice?2. The HATCHECK PROBLEM - In the 1940s a new restaurant employee checks the hats of n people without giving them claim check numbers.
When the customers return the checker returns the hats at random. What is the probability that nobody get the correct hat back? (In the language of permutations, what is the probability of a derangement?)3.
BIRTHDAY PROBLEM - In a random group of n people, what is the probability that at least one pair has the same birthday anniversary? How large must n be to make this probability greater than 50%?4.