staistics questions

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, 25% had asked for a raise, and of those women who had asked for a raise, 46% received the raise. If a woman is selected at random from the survey population of women, find the following probabilities

(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) p(woman asked for a raise)

 

This part is fairly simple as you just use the sample statistic of 25%

 

b) p(received raise | asked for one)

 

p(received raise | asked for one) = p(received raise and asked for one) / p(asked for one)

 

This statistic is already given as well: 46%

 

c) p(received raise and asked for one)

 

Rearrange the equation from part (b)

 

p(received raise and asked for one) = p(received raise | asked for one) * p(asked for one)

p(received raise and asked for one) = 0.46*0.25 = 11.5%