A system was set up in series with two components A and B In

A system was set up in series with two components, A and B. In order for the system to fail, only one must fail. The probability of failure for A is .30 and for B is .20. What is the probability of a system failure?

Solution

Probability of a system failure = P( One Must Fail) = 1 - P( Both in working condition) = 1 - [ (1-0.30) ( 1-0.20) ] = 1 - 0.56 = 0.44