Question: Find the probabilities for the following discrete random variables (20 pts)

a. A homeowner plants 6 bulbs selected at random from a box containing 5 tulip bulbs and 4 daffodil bulbs. What is the probability that the homeowner planted 2 daffodil bulbs and 4 tulip bulbs?

b. A couple decides that they will continue to have children until they have two males. Assuming that the P(male) = .5, what is the probability that their second male is their fourth child?

c. Suppose that 500 lottery tickets are sold. Among them, 200 tickets pay off at least the cost of the ticket. Now suppose you buy 5 tickets. Find the probability that you will win back at least the cost of 3 tickets.

d. A local drugstore owner knows that on average, 100 people per hour stop by his store

i. Find the probability that in a given 3 minute period nobody enters the store

ii. Find the probability that in a given 3 minute period more than 5 people enter the store