Question

Suppose the diagram of an electrical system is as given in Figure. What is the probability that the system works? Assume the components fail independently.

Answer 1

Solution

Is the probability that the system works?

By bypotheses \( \hspace{2mm}P(A)=0.95,P(B)=0.7,P(C)=0.8 \hspace{2mm}and \hspace{2mm}P(D)=0.9 \)

\( \implies P(A\cap B\cap C\cap D)=P(A)\times P(B\cup C)\times P(D) \)

                             \( =P(A)\times P(D)\bigg[P(A)+P(B)-P(B)\times P(C)\bigg] \)

                             \( =0.95\times 0.9(0.95+0.7+0.7\times 0.8)=0.8037 \)

Therefore. \( P(A\cap B\cap C\cap D)=0.8037 \)