Question

9. Provide two examples of variables with exhaustive and mutually exclusive values

Answer 1

Two events are mutually exhaustive if sum of the probabilities = 1

Example 1: consider rolling a dies. Let A be the even that the outcome is even and B be the event that the outcome is odd. A and B are mutually exhaustive.

Example 2: Consider a deck of cards. Let A be the event that a card drawn is red and B be the event that a card drawn is black. A and B are mutually exhaustive.

(The variables given above are mutually exclusive as well)

Two events are mutually exclusive if they both cannot occur at the same time

Example 1: Consider rolling a die. Let a be the event that outcome is less than 2 and B be the event that the outcome is greater than 4. The two events A and B are mutually exclusive.

Example 2: Consider tossing 2 coins: Let A be the event that both are heads and b be the event that both are tails. Then A and B are mutually exclusive.