Integrated Math 2 / Unit 9: Probability
9.4 The Addition Rule
Notes
For "or" probabilities, add and subtract the overlap.
- $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$.
- If events are mutually exclusive (cannot both happen), $P(A \text{ and } B) = 0$ and you just add.
- Example: a card from a deck is a heart or a king: $\displaystyle \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}$.
- The king of hearts is in both groups, so subtract it once.
Practice
$P(A) = 0.5$, $P(B) = 0.4$ and $P(A \text{ and } B) = 0.2$. What is $P(A \text{ or } B)$?
$0.5 + 0.4 - 0.2 = 0.7$.
One card is drawn from a standard 52-card deck. What is the probability it is a heart or a king?
$\displaystyle \frac{13 + 4 - 1}{52} = \frac{16}{52} = \frac{4}{13}$.
A fair die is rolled. What is the probability of rolling a 2 or a 5?
The events cannot both happen, so $\displaystyle \frac{1}{6} + \frac{1}{6} = \frac{1}{3}$.
Ready for more? Take the Unit 9 test.