An engineer gathered data on failures of a circuit that has

An engineer gathered data on failures of a circuit that has been considered for use in a satellite. After several experiments, the engineer decided that failures could be divided into the following mutually exclusive and exhaustive categories: A = integrated circuit failure; B = PC board failure; C = power supply failure; and D = other failure. The engineer also isolated a common problem of that is thought to contribute to all four types of failure. He established the following connections: P(A) = 0.40;P(M|A) = 0.05; P(B) - 0.25; P(M|B) = 0.05; P(C) = 0.30; P(M|C) = 0.04;P(D) = 0.05;P(M|D) = 0.01 Find P(M), P(M\'), P(C|M), P(C|M\') Interpret these events within their engineering context.

Solution

Solution :

P(M|A) P(A) = P(M and A) = 0.02

likewise P(M and B) = 0.0125 and P(M and C) = 0.012 and P(M and D) = 0.0005

=> P(M) = P(M and A)+P(M and B)+P(M and C)+P(M and D)
= 0.045
=> P(M \') = 1-P(M) = 0.955

P(C|M) = P(M and C) / P(M) = 0.012 / 0.045 = 4/15

P(C|M \') = P(M \' and C) / P(M \') = (P(C)-P(M and C))/P(M \')

= (0.30-0.012)/0.955 = 0.288/0.955 = 0.30157....