Question

Suppose A and B are two events such that P()=0.3 , P()=0.4 , and P(∩)=0.12 . Are events A and B independent? Justify your answer?

Answer 1

A and B are independent events because the product of their individual probabilities P(A)P(B) equals the probability of their intersection P(A AND B), which is both 0.12.

Step-by-step explanation:

The question asks whether two events A and B are independent. We are given that P(A) = 0.3, P(B) = 0.4, and P(A AND B) = 0.12. To determine if two events are independent, we need to check if the product of their individual probabilities equals the probability of their intersection. In mathematical terms, A and B are independent if P(A)P(B) = P(A AND B).

In this case, P(A)P(B) = 0.3 × 0.4 = 0.12. Since this product is equal to the given P(A AND B), which is also 0.12, it can be concluded that events A and B are independent.