# Probability (Complementary Events)

Probability shows the frequency or odds in which an random events should, theoretically, occur.

So, if you flip a coin, you have a $\dfrac{1}{2}$ probability of getting heads. See the lesson on Probability (single events) for more details.

In probability, "complementary events" are events that, if one occurs, the other definitely does not. Complementary events are also sometimes called "mutually exclusive" events.

So, when you flip a coin, getting heads ($\dfrac{1}{2}$) and getting tails ($\dfrac{1}{2}$) are complementary events.

You will either get heads or tails. If you get heads you definitely won't get tails.

If you roll a die, getting a 6 ($\dfrac{1}{6}$) and getting a 1, 2, 3, 4, or 5 (also known as not getting a 6) ($\dfrac{5}{6}$) are complementary events.

You will either get a 6, or some number other than 6. You can't get both 6 and non-6 (on one roll).

You might have also noticed that the probability of getting either of two complementary events will always add up to 1. You have a 100% chance of getting one of the 2 complementary events.

#### Practice Problems:

## Probability (Complementary events)

Find the complementary probability:

- If you flip a coin P(heads) is $\dfrac{1}{2}$. What is P(tails)?
- If you roll a die, P(5) is $\dfrac{1}{6}$. What is P(not 5)?
- If you roll a die, P(even number) is $\dfrac{1}{2}$. What is P(not even) or P(odd)?
- If your teachers is randomly choosing a student of the month, your probability of being chosen is $\dfrac{1}{32}$. What is the probability that you are not chosen?
- If your probability of winning a raffle is $\dfrac{1}{1,000}$, what is the probability that you do not win?
- If you randomly choose a student from a class, the probability that his or her favorite food is pizza is $\dfrac{5}{26}$. What is the probaility that, if you choose a random student from this class, what is the probability that his or her favorite food is something other than pizza?

#### Answer Key: