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)=(\mathbb P(R\cap P))/(\mathbb P(P))=(0.25)/(0.40)=0.625`