Question

Out of all fan items sent for refurbishing, 40% had mechanical defects, 50% had electrical defects and 25% had both. Denote A="fan item has a mechanical defect" and B="fan item has an electrical defect". Determine the probability that a fan item selected at random will have at least one defect.

Answer 1

Using Venn probabilities, it is found that there is a 0.65 = 65% probability that a fan item selected at random will have at least one defect.

What is a Venn probability?

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

The "or probability" is given by:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

In this problem, the given probabilities are $P(A) = 0.4, P(B) = 0.5, P(A \cap B) = 0.25$, hence, the "or probability", also called the "at least one" probability, is given by:

$P(A \cup B) = 0.4 + 0.5 - 0.25 = 0.65$

0.65 = 65% probability that a fan item selected at random will have at least one defect.

More can be learned about Venn probabilities at https://brainly.com/question/25698611