# If two events are mutually exclusive and collectively exhaustive, what is the probability that...

## Question:

If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur at the same time?

a. 0.

b. 0.50.

c. 1.00.

d. Cannot be determined from the information given.

## Mutually Exclusive and Collectively Exclusive Events:

Two events are said to be mutually exclusive if the happening of one event prevents the other event from happening. That is, if they both cannot happen at the same time. Two events are collectively exhaustive if at least one of the events must occur.

## Answer and Explanation:

The answer is: a. 0

An example of two events that are both mutually exhaustive and mutually exclusive is tossing a coin. When we toss a coin, we can only get a head (H) or a tail (T) but not head (H) and tail (T) at the same time.

In such a case, the probability of getting a head and a tail is equal to P(H and T) = 0 since the events are mutually exclusive and the probability of getting a head or a tail is P(H or T) = 1 since the events are mutually exhaustive.