AP Statistics / Unit 2: Probability, Random Variables, and Probability Distributions
2.6 Conditional Probability
Notes
$$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
- The probability of $A$ given that $B$ happened.
- Multiplication rule: $P(A\cap B)=P(B)\,P(A\mid B)$.
Practice
$P(A\cap B)=0.12$, $P(B)=0.4$. $P(A\mid B)=$
$\displaystyle \frac{0.12}{0.4}$.
Of 60 athletes, 15 wear glasses. Given a person is an athlete, $P(\text{glasses})=$
$\displaystyle \frac{15}{60}$.
$P(A\mid B)$ and $P(B\mid A)$ are:
The "given" changes the denominator.
Ready for more? Take the Unit 2 test.