A component is assembled in a four-step process. The probability of making a defect in step 1 is 10%; in step 2, 20%; in step 3, 8%; and in step 4, 5%. What is the probability that the component will be defective?

0.37072

Step-by-step explanation:

Let A be the event that step 1 is defective (P(A) = 10%), B the event that step 2 is defective(P(B) = 20%), C the event that step 3 is defective (P(C) = 8%), D the event that step 4 is defective(P(D) = 5%). Let us suppose that the occurance of a failure at any step is indepent of the other steps.

Recall the following properties

And given A, B, C, D independent , then

REcall that if the a set of events A,B,C,D are independent, their complements are also indepent.

Since we are asked for the probability of a defective item, this means that at least one of the steps is defective. Then, we are asked for the following probability: