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

Question:

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.