Question

As a company manager for claimstat corporation there is a 0.40 probability that you will be promoted this year. there is a 0.72 probability that you will get a promotion, a raise, or both. the probability of getting a promotion and a raise is 0.25. (1) if you get a promotion, what is the probability that you will also get a raise

Answer 1

Suppose $P$ denotes the event of getting promoted and $R$ the event of getting a raise. Then

$\mathbb P(P\cup R)=\mathbb P(P)+\mathbb P(R)-\mathbb P(P\cap R)$
$\implies0.72=0.40+\mathbb P(R)-0.25$
$\implies\mathbb P(R)=0.57$

Now it sounds like you're asked to find $\mathbb P(R\mid P)$, which the definition of conditional probability says is equivalent to

$\mathbb P(R\mid P)=\dfrac{\mathbb P(R\cap P)}{\mathbb P(P)}=\dfrac{0.25}{0.40}=0.625$