Question

A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are 0.01, 0.03, and 0.04, respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will not fail in one year?

Answer 1

0.9219 or 92.19%

Explanation:

The probability that the device will not fail in one year is given by the joint probability that none of the three components will fail within the year. The individual probabilities of not failing are:

`P(A) = 1-0.01 = 0.99\\P(B) = 1-0.03 = 0.97\\P(C) = 1-0.04 = 0.96`

The joint probability is:

`P(A \cap B\cap C) =0.99*0.97*9.96\\P(A \cap B\cap C) =0.9219 = 92.19\%`

There is a 0.9219 or 92.19% probability that the device will not fail in one year.