Compute At-least Probabilities
-A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.9, P(C) = 0.96, and P(D) = 0.98. Find the probability that at least one of the four parts will work.
A) 0.999992
B) 0.762048
C) 0.000008
D) 0.237952

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. So, for A and B, it's 1 - 0.9 = 0.1, for C it's 1 - 0.96 = 0.04, and for D it's 1 - 0.98 = 0.02. The probability that all fail is 0.1 * 0.1 * 0.04 * 0.02 = 0.000008. Therefore, the probability that at least one works is 1 - 0.000008 = 0.999992.

Compute At-Least Probabilities