Negative binomial distribution 5.11 A fair coin is tossed until heads appears four times. (a) Find the probability that it took exactly 10 flips. (b) Find the probability that it took at least 10 flips. (c) Let Y be the number of tails that occur. Find the pmf of Y . 5.12 Baseball teams A and B face each other in the World Series. For each game, the probability that A wins the game is p, independent of other games. Find the expected length of the series. 5.15 People whose blood type is O-negative are universal donorsanyone can receive a blood transfusion of O-negative blood. In the U.S., 7.2% of the people have O-negative blood. A blood donor clinic wants to find 10 O-negative individuals. In repeated screening, what is the chance of finding such individuals among the first 100 people screened? 5.17 Andy and Beth are playing a game worth $100. They take turns flipping a penny. The first person to get 10 heads will win. But they just realized that they have to be in math class right away and are forced to stop the game. Andy had four heads and Beth had seven heads. How should they divide the pot?