A Machine Has Four Components, A, B, C, and D

Multiple Choice

A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for themachine to work properly. Assume the probability of one part working does not depend on the functionality ofany of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.93,P(C) = 0.98, and P(D) = 0.96. Find the probability that at least one of the four parts will work. Round to sixdecimal places.

A) 0.999996
B) 0.813698
C) 0.000004
D) 0.186302