Question

What is the probability of $A$ or $B$?

Answer 1

Probability:

In probability, or means the occurrence of either of the events.

If $A$ and $B$ are the two events, then

$\mathit{P}\left(AorB\right)\mathbf{=}\mathit{P}\left(A\right)\mathbf{+}\mathit{P}\left(B\right)\mathbf{-}\mathit{P}\left(AandB\right)$

If $A$ and $B$ are mutually exclusive events, then

$\mathit{P}\left(AorB\right)\mathbf{=}\mathit{P}\left(A\right)\mathbf{+}\mathit{P}\left(B\right)$ $\left[\because P\left(AandB\right)=0\right]$

Hence, the probability of $\mathit{A}$ or $\mathit{B}$ is given by $\mathit{P}\left(AorB\right)\mathbf{=}\mathit{P}\left(A\right)\mathbf{+}\mathit{P}\left(B\right)\mathbf{-}\mathit{P}\left(AandB\right)$