# At a Glance - Complementary & Mutually Exclusive Events

Complementary events are two outcomes of an event that are the only two possible outcomes.

• This is like flipping a coin and getting heads or tails. Of course, there are no other options, so these events are complementary.
• Rolling a die and getting a 1 or 2 are not complementary, since there are other outcomes that may happen (3, 4, 5, or 6).
•  However, rolling a die and getting a 1 or not-a-1 are complementary (you have to roll either a 1 or not-a-1).

Mutually exclusive events are two or more outcomes of an event that cannot occur at the same time.

• Picking one card from a standard deck and choosing an ace or a king are mutually exclusive events (since you can't do both at the same time).
• However, choosing a red card or a king are not mutually exclusive (you could choose a red king).

All complementary events are mutually exclusive, but all mutually exclusive events are not necessarily complementary.

#### Instructions

 Let's note each Example as 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)

#### Example 1

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

#### Example 2

 Picking a coin from the piggy bank and getting a quarter or a coin divisible by 5. Mutually exclusive? NoComplementary? NoQuarters are also divisible by 5 (as well as dimes and nickels), so these are not mutually exclusive nor are they complementary.

#### Example 3

 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).

#### Exercise 1

Rolling a die and getting an odd number or a 4.

#### Exercise 2

Rolling a die and getting an even number or a four.

#### Exercise 3

Rolling a die and getting an odd number or an even number.