Let X ∼ Binomial(5, p) be the number of successes out of 5 independent trials. Denote a trial by S if it is a success, and by F if it is a failure. Consider the outcome SFFSS, in which the first trial is a success, the second trial is a failure, the third trial is a failure, and so on. Say whether each of the following statements is true or false. If the statement is false, say why.

a. P(SFFSS) = P(X = 3).

b. P(SFFSS) = 5 3

p 3 (1 − p)
2 .

c. P(SFFSS) = p 3 .

d. P(SFFSS) = p 3 (1 − p)
2 .