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Mutually Exclusive Events

Mutually Exclusive Events

Events are mutually exclusive when two events cannot happen at the same time.

For example, with an ordinary dice, it is not possible to throw an even number and an odd number at the same time: the two events are mutually exclusive. However, it is possible to throw an even number and a prime number (for example, 2) at the same time.

When more than one mutually exclusive event is being considered:

P(A) + P(B) = P(A + B)

The probability of an exhaustive set of mutually exclusive events add up to 1.

With an ordinary dice:

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1.

Example 1

Is this statement, for an ordinary six-sided dice, true?

P(even) + P(odd) = 1?

A dice will be either odd or even. This covers all possible events.

Answer: Yes

Example 2

A D12 (12-sided) dice is thrown. Are the events of rolling a prime number and rolling an even number, mutually exclusive?

A 2 is an even number and a prime number. The events can both happen on the same throw for the dice.

Answer: No