Complementary & Mutually Exclusive Events Examples

Using the images below, determine if each event is complementary, mutually exclusive, both, or neither.

Note: the piggy bank contains a quarter (25 cents), dime (10 cents), nickel (5 cents), and penny (1 cent).

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

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

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

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

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

Are they complementary? No. There are other options, like picking a penny or a quarter.

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

Are they mutually exclusive? No. Quarters are also divisible by 5 (as well as dimes and nickels), so these are not mutually exclusive.

Are they complementary? No. There are other options, like getting a penny.

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

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

Are they complementary? No. There are other options (like an orange one).

A bag has 8 neon green gumballs and 12 yellow gumballs. What is the probability of randomly picking out a neon green gumball, and is this event complementary?

The probability of getting a neon green gumball is or 40%.

When you grab a gumball from the bag, you will either get a neon green one or a yellow one. There is no other option, because we cleaned out all the lint before we put the gumballs in. So, this event is complementary.

The probability of pulling a blue marble randomly from the bag is or . What is the probability of picking a marble that is not blue?

Picking a marble that is not blue is complementary to picking a marble that is blue. Either the marbles are blue or they are not blue. So their probabilities add up to 1. Since the probability of picking a blue marble is , the probability of picking a marble that is not blue is or .