Problems

1. Suppose 30 people are in a room. What is the probability that at least two of them have the same birthday?

2. What is the probability of getting one pair in five-card draw poker?

3. What is the probability of getting two pairs in five-card draw poker?

4. In the game of keno, 80 balls (numbered 1–80) are mixed up, and then 20 balls are randomly drawn. Before the 20 balls are drawn, a player chooses 10 different numbers. If at least 5 of the numbers are drawn, the player wins. What is the probability of winning?

5. Going into the 2003 NBA finals, Jeff Sagarin rated San Antonio 3 points higher than New Jersey. The teams play until one team wins four games. The first two games were at San Antonio, the next three at New Jersey, and the final two games were scheduled for San Antonio. What is the probability that San Antonio will win the series?

6. What odds should the bookmaker give on Kansas winning the Final Four if the bookmaker wants to earn an average of 10 cents per dollar bet?