State True or False for the statements in the Exercise. Let P(A) 0 and P(B) 0. Then A and B can be both mutually exclusive and independent.

Question

State True or False for the statements in the Exercise. Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.

Philoid · Accepted Answer

FALSE

For events to be mutually exclusive –

P(A∪B) = P(A) + P(B)

But as per the conditions in question, it is not necessary that they will meet the condition because it might be possible that

P(A ∩ B) ≠ 0

For events to be independent–

P(A ∩ B) = P(A)P(B)

Again P(A) > 0 and P(B)> 0 are not sufficient conditions to validate them.

Tip: you can also check by considering any simple example