Candidates for a job are interviewed one by one until a qualified candidate is found. Thirty percent of the candidates are qualified.
a. What is the probability that the first candidate is qualified?
b. What is the probability that the first candidate is unqualified and the second candidate is qualified?
c. LetX represent the number of candidates interviewed up to and including the first qualified candidate. Find P(X=4).
d. Find the probability mass function of X.
Let Q denote a qualified candidate, and U an unqualified one.
(a) P(Q) = 0.3
(b) P(UQ) = P(U)P(Q) = (0.7)(0.3) = 0.21
(c) P(X = 3) = P(UU A) = P(U)P(U)P(A) = (0.7)(0.7)(0.3) = 0.147
(d) 
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