For question a-e, please write down the type of distribution (eg. Poisson's, binomial, etc.) and the associated parameters. Then, answer the question. (Please write down all working/calculations + explanation, thank you so much!)

Question: On average, 9 babies are born on a 24-hour day at a hospital.

a) What is the probability that at least one baby will be born today on the 8am-4pm shift?

b) What is the probability that exactly 4 babies will be born on the 8am-4pm shift?

c) What is the probability that exactly 4 babies will be born on one of the next three 8-hour shifts?

d) What is the probability that you will have to wait for three 8-hour shifts until you get the first one with exactly 4 babies born?

e) What is the probability that you will have to wait for three 8-hour shifts until you get the second one with exactly 4 babies born?