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?
(2) Are getting a raise and being promoted independent events? Explain using probabilities.
(3) Are these two events mutually exclusive? Explain using probabilities.

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

25% or 0.25

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

yes, they are independent events because you a given one probability for getting a raise (40%) and another one for getting both a raise and a promotion (25%). If they were dependent events, the probability would be the same but they are not.

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

No they are not, again the probability of getting both a raise and a promotion is 25%.  

the investment was $14,174.196

explanation:

a lump sum means that the father of the example made one deposit and leave it be.

we need to know the value of a capital that generated at 4.05% per year during 28 years the sum of $48,613.24

now clearing the formula to solve for capital we got:

and we reach the answer investment = $14,174.20

answer; organizational;