Question

3. As a company manager for Claimstat Corporation there is a 0.40 probability that you will be promoted this year. There is a 0.6 probability that you will get a promotion, a raise, or both. The probability of getting a promotion and a raise is 0.3.

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

(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

a)

P( Raise | Promotion ) = P(Raise AND promotion ) / P(Promotion)

= 0.3 / 0.4

= 0.75

b)

Using addition rule,

P(Raise OR promotion ) = P(raise) + P(Promotion) - P(Raise AND promotion )

0.6 = P(Raise) + 0.4 - 0.3

P(Raise) = 0.5

Two events are independent if,

P(Raise AND promotion ) = P(raise) * P(promotion)

P(Raise AND promotion ) = 0.3

P(raise) * P(promotion) = 0.5 * 0.4 = 0.2

P(Raise AND promotion ) P(raise) * P(promotion)

So, events are not independent.

c)

Two events are mutually exclusive if P(A and B) = 0

Since

P(Raise AND promotion ) = 0.3 0

Events are not mutually exclusive.