If events X and Y are mutually exclusive, P(X) = 1/3 and P(Y) = 2/5, P(X∪Y) is

If events X and Y are mutually exclusive, P(X) = 1/3 and P(Y) = 2/5, P(X∪Y) is

Answer Details

If events X and Y are mutually exclusive, it means they cannot occur at the same time. In other words, if X happens, Y cannot happen, and vice versa. This also means that the probability of both events happening at the same time (P(X∩Y)) is equal to zero. We can use the formula for the probability of the union of two events: P(X∪Y) = P(X) + P(Y) - P(X∩Y) Since X and Y are mutually exclusive, we know that P(X∩Y) is equal to zero: P(X∪Y) = P(X) + P(Y) - 0 We can substitute the given probabilities into this formula: P(X∪Y) = 1/3 + 2/5 To add these fractions, we need a common denominator. The smallest common multiple of 3 and 5 is 15, so we can rewrite the fractions with this denominator: P(X∪Y) = 5/15 + 6/15 P(X∪Y) = 11/15 Therefore, the answer is 11/15.