Algebra 2 / Unit 9: Probability
9.5 Independent and Dependent Events
Notes
- Independent events don't affect each other: $P(A \text{ and } B) = P(A) \cdot P(B)$.
- Dependent events do: $P(A \text{ and } B) = P(A) \cdot P(B \mid A)$.
- Drawing without replacement makes events dependent: the second draw has one fewer item.
- Example: two red cards in a row from a deck without replacement: $\displaystyle \frac{26}{52} \cdot \frac{25}{51} = \frac{25}{102}$.
- Test for independence: check whether $P(A \text{ and } B) = P(A) \cdot P(B)$.
Practice
A coin is flipped and a die is rolled. What is $P(\text{heads and a } 4)$?
Independent: $\displaystyle \frac{1}{2} \cdot \frac{1}{6} = \frac{1}{12}$.
A bag has 5 red and 3 blue marbles. Two are drawn without replacement. What is $P(\text{both red})$?
$\displaystyle \frac{5}{8} \cdot \frac{4}{7} = \frac{20}{56} = \frac{5}{14}$.
$P(A) = 0.4$, $P(B) = 0.5$ and $P(A \text{ and } B) = 0.2$. Are $A$ and $B$ independent?
Independence means $P(A \text{ and } B) = P(A)P(B)$.
Ready for more? Take the Unit 9 test.