As a company manager there is a 35% probability that you will be promoted this y

Question

As a company manager there is a 35% probability that you will be promoted this year. There is a 64% probability that you will get a promotion, a raise or both. The probability that you will get a promotion and a raise is 17%.

If you get a promotion, what is the probability that you will also get a raise? Enter your answer in blank #1. (Round your answer to 3 decimal places and enter your answer as 0.123, not .123.)

What is the probability that you will get a raise? Enter your answer in blank #2.  (Round your answer to 2 decimal places and enter your answer as 0.12, not .12.)

Are the events "getting promoted" and "getting a raise" independent? Enter "yes" or "no" in blank #3.

Are the events "getting promoted" and "getting a raise" mutually exclusive? Enter "yes" or "no" in blank #4.

Explanation / Answer

Here we are given that: P( Promotion ) = 0.35,

P( Promotion or raise ) = 0.64

P( Promotion and raise ) = 0.17

a) Given that we got a promotion, probability that there will also be a raise is computed as: ( Using Bayes theorem )

P ( raise | promotion ) = P( Promotion and raise ) / P( Promotion ) = 0.17 / 0.35 = 0.486

Therefore 0.486 is the required probability here.

b) Using addition law of probability we get:

P( Promotion or raise ) = P( Promotion ) + P( raise ) - P( Promotion and raise )

Putting all the values we get:

0.64 = 0.35 + P( raise ) - 0.17

P( raise ) = 0.64 - 0.35 + 0.17 = 0.46

Therefore 0.46 is the required probability here.

c) P( promotion ) = 0.35, P( raise ) = 0.46

P( promotion ) P( raise ) = 0.35*0.46 = 0.161

P( Promotion and raise ) = 0.17

Therefore P( Promotion and raise ) is not equal to P( promotion ) P( raise )

Therefore the events "getting promoted" and " getting a raise " are not independent events.

d) P( Promotion and raise ) = 0.17 which is not equal to 0

Therefore the events "getting promoted" and " getting a raise " are not mutually exclusive.

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