Chapter 5.3, Problem 28P

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

1. (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.
2. (b) Explain why P(r ≥ 1) = 1 – P(0).
3. (c) Explain why P(r ≥ 2) = 1 – P(0) – P(1).
4. (d) Explain why P(r ≥ m) = 1 – P(0) – P(1) – … –P(m–1) for 1 ≤ m ≤ n.