A machine has two parts 1 and 2 arranged in parallel The mac

A machine has two parts 1 and 2 arranged in parallel. The machine will only fail if both these components fail. What are the chances that machine will NOT fail if probabilities of failure of component 1 and 2 are 0.05 and 0.15, respectively? In this case, 1 and 2 are not independent and probability of failure of 1 given that 2 has already failed is 0.3.

Hint: P(AB)= P(A).P(B|A)

Solution

What are the chances that machine will NOT fail if probabilities of failure of component 1 and 2 are 0.05 and 0.15, respectively?

P( 1 failed / 2 failed) = 0..3

P( 1 failed and 2 failed ) = 0.05 * 0.3 = 0.015

Probability that will not fail is 1 - 0.015 = 0.985