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math: add conditional probability

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eggy 2021-03-09 18:19:04 -05:00
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Events $A$ and $B$ are **exhaustive** if their union includes all possible outcomes in the sample space: $A\cup B=U$. Events $A$ and $B$ are **exhaustive** if their union includes all possible outcomes in the sample space: $A\cup B=U$.
$$P(A\cup B)=1$$ $$P(A\cup B)=1$$
The **principle of inclusion and exclusion** forms a general rule for the union between two sets: The **principle of inclusion and exclusion** forms a general rule for the union between two *independent* events:
$$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$ $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
### Conditional probability
A vertical bar is used between two events to denote that the event on the left occurs knowing that the right has already occurred.
$$P(A|B) = \frac{P(A\cap B)}{P(B)}$$
!!! example
$P(A|B)$ is the probability of event $A$ given $B$ has occurred.
## Resources ## Resources
- [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf) - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)