 # What Is a Conditional Probability?

Conditional probability entails that events affect each other. This means that the probability of one event changes if you know that another event has occurred. $P\phantom{\rule{-0.17em}{0ex}}\left(A\mid B\right)$ is the probability of $A$ occurring given that you “know” that $B$ has already occurred. You can find it with this formula:

 $P\phantom{\rule{-0.17em}{0ex}}\left(A\mid B\right)=\frac{P\phantom{\rule{-0.17em}{0ex}}\left(A\cap B\right)}{P\phantom{\rule{-0.17em}{0ex}}\left(B\right)}$

Example 1

In Nick’s class, $\text{}50\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ of the students like sushi, and $\text{}30\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ like both sushi and kebab. If you know that Nick likes sushi, what is the probability of him also liking kebab?

Let $A$ be the event “Nick likes kebab”, and let $B$ be the event “Nick likes sushi”. Then you’ll have to find $P\phantom{\rule{-0.17em}{0ex}}\left(A\mid B\right)$. Using the formula above, you get

 $\frac{P\phantom{\rule{-0.17em}{0ex}}\left(A\cap B\right)}{P\phantom{\rule{-0.17em}{0ex}}\left(B\right)}=\frac{0.3}{0.5}=0.6,$

which tells you that the conditional probability of Nick liking kebab given that he likes sushi is $60$ %.