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

Question

Quizplus · Accepted Answer

The probability that at least one of the four parts will work is calculated by subtracting the probability that none of the parts work from 1. The probability that a part fails is 1 minus the probability that it works. Therefore, the probability that all parts fail is (1 - 0.93) * (1 - 0.93) * (1 - 0.98) * (1 - 0.96) = 0.07 * 0.07 * 0.02 * 0.04. Subtracting this product from 1 gives the probability that at least one part works, which is very close to 1, indicating a very high probability that at least one component will function.

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