Answer to Question #102015 in Statistics and Probability for Doniyor

Question

A campus student club distributed material about membership to new students attending an orientation meeting. Of those receiving this material 40% were men and 60% were women. Subsequently, it was found that 7% of the men and 9% of the women who received this material joined the club.
a. Find the probability that a randomly chosen new
student who receives the membership material will join the club.
b. Find the probability that a randomly chosen new student who joins the club after receiving the membership material is a woman.

Answer 1

a.

$P(men)=0.4, \ P(women)=0.6,$

$P(join|men)=0.07, \ P(join|women)=0.09$

$$P(join)=P(men)P(join|men)+P(women)P(join|women)$$

$$P(join)=0.4(0.07)+0.6(0.09)=0.082$$

b.

$$P(women|join)={P(women)P(join|women) \over P(join)}$$

$$P(women|join)={0.6(0.09) \over 0.082}={27 \over 41}\approx0.659$$