Question

An electronic product contains 40 integrated circuits. the probability that any integrated circuit is defective is 0.01, and the integrated circuits are independent. the product operates only if there are no defective integrated circuits. what is the probability that the product operates?

Answer 1

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.