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Basic Statistics & Probability

Basic Statistics & Probability

Complementary & Mutually Exclusive Events Examples

Example 1

Let's note each Example as complementary, mutually exclusive, both, or neither.

piggy bank

Note: the piggy bank contains a Quarter (25 cents), Dime (10 cents), Nickel (5 cents), and Penny (1 cent)

Example 2

Picking one coin from the piggy bank and getting a dime or a nickel.

Mutually exclusive? Yes. You can't pick a dime and a nickel at the same time

Complementary? No. There are other options, like a penny or quarter

Example 3

Picking a coin from the piggy bank and getting a quarter or a coin divisible by 5.

Mutually exclusive? No

Complementary? No

Quarters are also divisible by 5 (as well as dimes and nickels), so these are not mutually exclusive nor are they complementary.

Example 4

Choosing one marble from the bag and getting a blue or a green one.

Mutually exclusive? Yes. You can't choose a marble that is both blue and green at the same time.

Complementary? No. There are other options (like an orange one).