Question

How do you find conditional probability?

Answer 1

Definition of conditional probability:

The probability of happening of an event $A$when another event $B$related to $A$has already happened is called conditional probability and is denoted by$P\left(A/B\right)$.

The formula to find conditional probability is given by:

$\mathit{P}\left(\frac{A}{B}\right)\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{P}\mathbf{(}\mathbf{A}\mathbf{\cap }\mathbf{B}\mathbf{)}}{\mathbf{P}\mathbf{\left(}\mathbf{B}\mathbf{\right)}}$

For example:

A coin is tossed three times, If given that an event that shows the first toss was head, then what is the probability of three heads.

let $B$is the event that shows the first toss is head and $A$is the event of an occurrence of three heads

$B=\left\{HHH,HHT,HTH,HTT\right\}$ and $A=\left\{HHH\right\}$

So, $A\cap B=\left\{HHH\right\}$

Then $P($getting $3$heads given that first toss is head$)$, or

$P\left(\frac{A}{B}\right)=\frac{P(A\cap B)}{P\left(B\right)}=\frac{1}{4}$