6. Using the information in problem #1, what is the probability that exactly 25 items will be chosen randomly to observe the first defective item? 7. Assume that blood types are distributed in the population as follows: 30% type A; 20% type B; 15% type AB; 35% type O. A blood bank needs 5 type O donors. Let X be the number of persons needed to be tested to find exactly 5 type O donors. (a) What is the pmf of X? (b) Find the probability that 8 people need to be tested to find 5 type O donors. (c) What is the expected number of people needed to be tested to findle type O donors? (d) What is the probability that fewer than 20 people need to be tested to find exactly 1 type AB donor? 8. Suppose the Atlanta Braves compete against the Boston Red Sox in the 2018 World Series. And suppose it is assumed that the probability that the Braves will defeat the Red Sox in any single game is .44. (In the past several years in head to head competition, the Braves have won 32 games and the Red Sox have won 40 games.) A team wins the World Series if it wins 4 out of 7 games. (a) What is the probability that the Red Sox will win the series in 6 games? (b) What is the probability that the Braves will win the Series in 7 games? (c) What is the probability the Red Sox will win the Series