Question

In: Statistics and Probability

Probability

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.

Solutions

Expert Solution

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

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