For each of the following situations state whether or not a binomial would be an appropriate probability model for the variable Y and explain why.
(a) Seeds of the garden pea (Pisum sativum) are either yellow or green. A certain cross between pea plants produces progeny that are in the ratio 3 yellow: 1 green. Suppose your goal is to get 3 yellow, but you don't care how many green you get. You sample, one at a time, until you have exactly 3 progeny that are yellow. Let Y be the number of progeny you have to observe in order to get 3 yellow. Is Y a binomial random variable? Why or why not?
(b) Some people exercise every day, some exercise occasionally, and some never exercise. Suppose you take a random sample of 45 people and ask each of them how often they exercise. Let Y be the number of people, out of 45, who exercise every day. Is Y a binomial random variable? Why or why not?