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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

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Suppose [tex]P[/tex] denotes the event of getting promoted and [tex]R[/tex] the event of getting a raise. Then

[tex]\mathbb P(P\cup R)=\mathbb P(P)+\mathbb P(R)-\mathbb P(P\cap R)[/tex]
[tex]\implies0.72=0.40+\mathbb P(R)-0.25[/tex]
[tex]\implies\mathbb P(R)=0.57[/tex]

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

[tex]\mathbb P(R\mid P)=\dfrac{\mathbb P(R\cap P)}{\mathbb P(P)}=\dfrac{0.25}{0.40}=0.625[/tex]

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