1. Yizhang and Cheryl were waiting for Prof. to come for a meeting. Yizhang proposed a bet. He said that he would toss a fair coin 100 times, and if it landed tails more than 60 times, he would give Cheryl $5, otherwise Cheryl would give him $5...but Cheryl did not want to do. She was not sure that the coin was fair, and proposed the following test - Yizhang would toss the coin 30 times, and she would see how many times the coin landed tails, and then decide.

• (a) How many times would you expect the coin to land tails in 30 tosses?
• (b) If the coin lands tails 10 times, should Cheryl play? (Figure out the probability that the coin will land tails ten times, if the coin is fair.)