Let’s define two events a and B in the same sample space. Their probabilities are as follows:

Question

P(A) = 0.5
P(B) = 0.6
Is it possible for events A and B to be disjoint?

Answer 1

No, it is not possible for events A and B to be disjoint if their probabilities are both greater than zero. Disjoint events, also known as mutually exclusive events, are events that cannot occur at the same time. In other words, if events A and B are disjoint, then the probability of both events occurring together is zero (P(A ∩ B) = 0). However, since both P(A) and P(B) are greater than zero, it means that there is a non-zero probability of A and B occurring together, which means they are not disjoint.