Question

An assembly consists of three mechanical components. Suppose that the probabilities that the first, second, and third components meet specifications are 0.95, 0.96, and 0.98. Assume that the components are independent. Let X be the number of components that meet specifications. Determine the probability mass function of X. Round your answers to five decimal places (e.g. 98.76543).

P(X=0)
P(X=1)
P(X=2)
P(X=3)

Answer 1

P(X = 0) = (0.05)(0.02)(0.01) = 0.00001
P(X = 1) = (0.95)(0.02)(0.01) + (0.05)(0.98)(0.01) +(0.05)(0.02)(0.99) = 0.00167
P(X = 2) = (0.95)(0.98)(0.01) + (0.95)(0.02)(0.99) +(0.05)(0.98)(0.99) =0.07663
P(X = 3) = (0.95)(0.98)(0.99) = 0.92169