1. What is the probability that, in a group of 25 people, at least one person has a birthday on June 13? Why is your answer different from the probability displayed in Table 1 for r = 25?
2. Johnny Carson, host of The Tonight Show from 1962-1992, discussed the birthday problem during one of his monologues. To test the hypothesis, he asked the audience whether any of them were born on his birthday, October 23. Carson was surprised that no one in the audience of 100 people shared his birthday. What was wrong with Carson's reasoning? What is the probability that one or more people in the audience were born on October 23?