Question: General: Probability Formula

Let r be a binomial random variable representing the number of successes out of n trials.

a.) Explain why the sample space for r consists of the set (0, 1, 2 …,n) and why the sum of the probabilities of all the entries in the entire sample space must be 1.

b.) Explain why P(r ≥ 1) = 1 – P(0)

c.) Explain why P(r ≥ 2) = 1 – P(0) – P(1)

d.) Explain why P(r ≥ m) = 1 – P(0) – P(1) - … - P(m – 1) for 1 ≤ m ≤ n