Critical Thinking 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 P1r  12 5 1  P102.

(c) Explain why P1r  22 5 1  P102  P112.

(d) Explain why P1r  m2 51P102 P112   P1m12 for 1  m  n.