Question

4. 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 0.28.

(1) If you get a promotion, what is the probability that you will also get a raise?

(2) Are getting a raise and being promoted independent events? Explain using probabilities.

(3) Are these two events mutually exclusive? Explain using probabilities.

Answer 1

P(Proportion) = 0.40 , P(promotion or rise) = 0.72 , P(promotion and rise) = 0.28

a)

P(rise | promotion ) = P(promotion and rise) / P(promotion)

= 0.28 / 0.40

= 0.70

b)

P(promotion or rise) = P(Proportion) + P(Rise) - P(promotion and rise)

P(Rise) = P(promotion or rise) - P(Proportion) + P(promotion and rise)  

= 0.72 - 0.40 + 0.28

= 0.84

The events rise and promotion are independent if

P(promotion and rise) = P(Promotion ) * P(Rise)

Now,

P(Promotion ) * P(Rise) = 0.72 * 0.84

= 0.6048

So

P(promotion and rise) P(Promotion ) * P(Rise)

The events rise and promotion are not independent.

c)

The events rise and promotion are mutually exclusive if

P(promotion and rise) = 0

Since P(promotion and rise) = 0.28 0

The events rise and promotion are not mutually exclusive.