Does it pay to ask for a raise? A national survey of heads of households showed

Question

Does it pay to ask for a raise? A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one. According to the survey, of the men interviewed, 20% had asked for a raise and 61% of the men who had asked for a raise received the raise. If a man is selected at random from the survey population of men, find the following probabilities. (Enter your answers to three decimal places.)

(a) P(man asked for a raise)


(b) P(man received raise, given he asked for one)


(c) P(man asked for raise and received raise)

Explanation / Answer

a)

P( Man asked for raise) = 0.20 (directly viven in question)

b)

P(man received raise, given he asked for one) = 0.61 (Directly given in question)

c)

P(man asked for raise and received raise) = ?

We use conditioal probability formula here

P(A | B) = P (A AND B) / P(B)

Therefore

P(A AND B) = P( A | B) * P( B)

Similllarly,

P(man asked for raise and received raise)=P(man received raise, given he asked for one)* P( Man asked for raise)

= 0.61 * 0.20

= 0.122

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