Algebra 2 / Unit 9: Probability
9.4 Probability and Compound Events
Notes
For equally likely outcomes, $\displaystyle P(A) = \frac{\text{favorable outcomes}}{\text{total outcomes}}$.
- Complement: $P(\text{not } A) = 1 - P(A)$. Useful for "at least one."
- Or rule: $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$.
- Mutually exclusive events can't happen together, so $P(A \text{ and } B) = 0$.
- Example: rolling a die, $\displaystyle P(\text{even or } > 4) = \frac{3}{6} + \frac{2}{6} - \frac{1}{6} = \frac{4}{6}$.
Practice
One card is drawn from a standard 52-card deck. Find $P(\text{heart or king})$.
$\displaystyle \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52}$. Don't count the king of hearts twice.
A die is rolled twice. What is the probability of at least one 6?
$\displaystyle 1 - \left(\frac{5}{6}\right)^2 = 1 - \frac{25}{36} = \frac{11}{36}$.
Events $A$ and $B$ are mutually exclusive with $P(A) = 0.3$ and $P(B) = 0.5$. Find $P(A \text{ or } B)$.
They can't overlap, so just add.
Ready for more? Take the Unit 9 test.