We are given that the
operation of all circuits is independent with each other, therefore we can use
the multiplication rule for independent events, which states that P (intersection
of A and B) = P(A) * P(B). In this case, we want the intersection of circuit 1 to
be working with the intersection of circuit 2 on and on until circuit 40. That
is, we want every circuit to work with each other. The given probability that
circuit 1 works is .99. The probability that circuit 2 works is still .99 since
this is independent events. And we see that the probability for each of the 40
circuit to work is .99.
So P (intersection of 1 through 40) = .99 * .99 *
.99.....*.99 = (.99)^40 = .6689717586
Answer:
There is a 0.67 probability (or 67%) that the product will work.
