A machine has four components, A, B, C, and D, set up in such a manner that all

Question

A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) =0.95, P(B) = 0.94, P(C) = 0.91, and P(D) = 0.95. Find the probability that all the parts work properly.

{Answer Format: Round the answer to THREE decimal places. Example: If answer is 0.86575, enter 0.866}

Explanation / Answer

Here we have given that

P(A)= 0.95

P(B) = 0.94

P(C) = 0.91

P(D) = 0.95

Now we want to find the all parts work properly.

that is we get

P( All parts work properly )= P( A) * P(B) * P(C) * P(D)

= 0.95*0.94 * 0.91 * 0.95

=0.772

that is we get

Probablity that all the parts work properly is 0.772

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