A doubt on independent events in probability

Question

A article manufactured by a company consists of 3 component A, B, C. These components are manufactured by 3 independent processes. The probability of these components being defective in the process of manufacture are 0.04, 0.03, 0.05 respectively. what is the probability of the assembled article being defective?

To answer this question, I thought that P(AnBnC)= P(A).P(B).P(C)= 0.00006 is the answer since these 3 components are independent.

So I need help whether the answer is correct or wrong and if its wrong then how to get the correct answer?

Answer 1

It depends on the definition of defective article, which is not given clearly in the problem. If the article is defective in case when the three elements are defective the answer is correct. If the article is defective when at least one of the elements is defective the answer is not correct. In this case the formula given by @user2661923 is correct.

Answer 2

I'd expect that the product is defective if any of the components are defective, not all of them.

Let $D$ be the event the product is defective, then $D = A \cup B \cup C$

So, $$P(D) = P(A \cup B \cup C) = 1-P(A^c \cap B^c \cap C^c)=$$ $$1-(1-P(A))(1-P(B))(1-P(C)) = 1-(.96)(.97)(.95) = 11.54\%$$