Question

What does Intersection mean in probability?

Answer 1

Key words in Probability:

The intersection of two sets $A$ and $B$ is a set that contains common elements of both sets. It is denoted by $A\cap B$.

In probability, $A\cap B$ means both events $A$ and $B$ will occur.

Formulas:

1. $\mathit{P}\left(A\cap B\right)\mathbf{=}\mathit{P}\left(A\right)\mathbf{+}\mathit{P}\left(B\right)\mathbf{-}\mathit{P}\left(A\cup B\right)$ When $A$ and $B$ are dependent events
2. $\mathit{P}\left(A\cap B\right)\mathbf{=}\mathit{P}\left(A\right)\mathbf{·}\mathit{P}\left(B\right)$, When $A$ and $B$ are independent events.
3. Conditional probability: $\mathit{P}\left(A\cap B\right)\mathbf{=}\mathit{P}\left(B\right)\mathit{P}\left(A|B\right)$

Hence, the meaning of intersection is explained