Probability of occurrence of an event A is 1 2 and that of B is 3 10 . If A and B are mutually exclusive, then the probability of occurrence of neither A nor B is

Step-by-step solution

Given P(A) = 1 2 and P(B) = 3 10 . Since A and B are mutually exclusive events, P(A B) = 0 . The probability of occurrence of either A or B is given by P(A B) = P(A) + P(B) - P(A B) . Substituting the values, P(A B) = 1 2 + 3 10 - 0 = 5 + 3 10 = 8 10 = 4 5 . The probability of occurrence of neither A nor B is P(A' B') = 1 - P(A B) . P(A' B') = 1 - 4 5 = 1 5 . Answer: 1 5