AP Statistics / Unit 2: Probability, Random Variables, and Probability Distributions
2.7 Independent Events and Unions of Events
Notes
- $A$ and $B$ are independent if $P(A\mid B)=P(A)$. Then $P(A\cap B)=P(A)P(B)$.
- General addition rule: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.
Practice
$P(A)=0.5$, $P(B)=0.4$, independent. $P(A\text{ and }B)=$
Multiply.
$P(A)=0.5$, $P(B)=0.4$, $P(A\cap B)=0.1$. $P(A\cup B)=$
$0.5+0.4-0.1$.
Can two events with positive probability be both mutually exclusive and independent?
If one happens, the other can't, so it changes the probability.
Ready for more? Take the Unit 2 test.