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 women interviewed, 26% had asked for a raise, and of those women who had asked for a raise, 45% received the raise. If a woman is selected at random from the survey population of women, find the following probabilities. (Enter your answers to three decimal places.)

(a) P (woman asked for a raise)

(b) P (woman received raise, given she asked for one)

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

Answer: (a) 0.26 (26%)

(b) 0.45 (45%)

(c) 0.117 (11.7%)

Step-by-step explanation:

(a) P (woman asked for a raise) = 0.26

This part is given in the question as 26% (The sample statistic). This is the proportion of women who asked for a raise.

(b) P (received raise given she asked)

This is a conditional probability question, as we are looking for the chance that a woman received a raise given she already asked for one.

P (received raise/asked for one) = P (received raise and asked for one) / P (asked for one)

= (0.26 x 0.45) / 0.26

= 0.45

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

This is a Joint probability and it is found by multiplying the the probability that she received a raise given she asked for one by the probability that she asked for one. This can be deduced by rearranging the conditional probability formula in (b) above.

= P (received raise / she asked for one) x P (asked for one)

= 0.45 x 0.26

= 0.117