Answer
$P(X=0) = 0.001$
$P(X=1) = 0.068$
$P(X=2) = 0.931$
Work Step by Step
Let X = event that x number of parts meet specifications. For component A, probability of meeting specifications is 0.95, so the probability of defect is 1-0.95 = 0.05; and for component B, the probability of meeting specifications is 0.98 and so the probability of defect is 1-0.98 = 0.02. The probability mass function is given by the following:
P(X=0) = Prob(x=0 parts meet specifications, both defective) = (0.02)(0.05) = 0.001
P(X=1) = Prob(x=1 part meets specifications, either A or B) = (0.95)(0.02)+(0.05)(0.98) = 0.068
P(X=2) = Prob(x=2, both parts meet specifications) = (0.98)(0.95) because they are independent = 0.931
