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Combined Events: OR

For mutually exclusive events, the probability of A or B is simply P(A) + P(B).

Either One or the Other

Example 1 — OR with a die

A standard die is rolled. Find P(rolling a 2 or a 5). 1 These outcomes cannot both happen on one roll — they are mutually exclusive 2 P(2) = \frac{1}{6}, P(5) = \frac{1}{6} 3 Add: \frac{1}{6} + \frac{1}{6} = \frac{2}{6} Answer: \frac{1}{3}

Example 2 — OR with a bag of balls

A bag has 4 red, 3 blue, and 2 green balls (9 total). Find P(red or green). 1 Drawing one ball can only be one colour — red and green are mutually exclusive 2 P(red) = \frac{4}{9}, P(green) = \frac{2}{9} 3 Add: \frac{4}{9} + \frac{2}{9} = \frac{6}{9} Answer: \frac{2}{3}

Practice

A bag has 5 red, 3 blue, and 2 yellow balls (10 total). Find P(blue or yellow) as a decimal.

Your answer

Either One or the Other

Example 1 — OR with a die

A standard die is rolled. Find P(rolling a 2 or a 5). 1 These outcomes cannot both happen on one roll — they are mutually exclusive 2 P(2) = \frac{1}{6}, P(5) = \frac{1}{6} 3 Add: \frac{1}{6} + \frac{1}{6} = \frac{2}{6} Answer: \frac{1}{3}

Example 2 — OR with a bag of balls

A bag has 4 red, 3 blue, and 2 green balls (9 total). Find P(red or green). 1 Drawing one ball can only be one colour — red and green are mutually exclusive 2 P(red) = \frac{4}{9}, P(green) = \frac{2}{9} 3 Add: \frac{4}{9} + \frac{2}{9} = \frac{6}{9} Answer: \frac{2}{3}

Practice

A bag has 5 red, 3 blue, and 2 yellow balls (10 total). Find P(blue or yellow) as a decimal.

Your answer