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 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 1

(a)

From the given data, the following Table is calculated:

	Asked for a raise	Did not ask for a raise	Total
Received the raise	0.26 X 0.45 = 0.117
Did not receive the raise	0.26 - 0.117 = 0.143
Total	0.26	1 - 0.26 = 0.74	1.00

P(Woman asked for a raise) = 0.26

So,

Answer is:

0.26

(b)
P(Woman received raise/ Asked for a raise) = P(Woman received raise AND Asked for a raise)/ P(Asked for a raise)

                                                                       = 0.117/0.26

                                                                        = 0.45

So,

Answer is:

0.45

(c)

P(Woman asked for a raise AND received it) = 0.117

So,

Answer is:

0.117