If two events are mutually exclusive, then show that they have no outcomes in common.

The definition of the mutually exclusive event itself states, that two events are mutually exclusive if they cannot occur at the same time.

Answer: Proved that if two events are mutually exclusive, they cannot have any common outcomes. 

Read the example and understand the feasibility of the statement given in the question.

Explanation:

The definition of the mutually exclusive event, itself states, that two events are mutually exclusive if they cannot occur at the same time.

This means that they do not share any common outcomes, P(A|B) = 0

For example, suppose the sample space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Let A = {1, 2, 3, 5}, B = {5, 6, 7, 8}, and C = {7, 9}.

1. A and B = {5}. P (A ∩ B) = 1/10 ≠ 0. Therefore, A and B are not mutually exclusive.
2. A and C do not have any numbers in common, so P (A ∩ C) = 0. Therefore, A and C are mutually exclusive.

Hence, if two events are mutually exclusive, they cannot have any common outcomes.