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)

Accepted Solution

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 ) = 0.26This 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