Question

As a company manager for the Quick Money Business 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 or a raise. The probability of getting a promotion and a raise is 0.25. If you get a promotion, what is the probability that you will get a raise?

Answer 1

Probability of getting raise when you get promoted = 0.625

Explanation:

We have to find the probability of getting a raise. So,

Promotion = P, Raise = R

First we find if you get the promotion, what is the probability that you will also get a raise

`P(R | P) = (P(P \& R))/(P(P)) = \frac {0.25}{0.4} = 0.625`

Probability of getting raise when you get promoted = 0.625.

Now we find the probability of getting a raise,

`P(P\ or\ R) = P(P) + P(R) - P(P \& R)\\\0.72 = 0.4 + P(R) - 0.25\\P(R) = 0.72 - 0.4 +0.25\\P(R) = 0.57`

So, the probability of getting raise = 0.57.