Question

A campus student club distributed material about membership to new students attending an orientation meeting. Of those receiving this material, 35​% were men and 65​% were women.​ Subsequently, it was found that 8​% of the men and 11​% of the women who received this material joined the club. Complete parts a and b below.

a. Find the probability that a randomly chosen new student who receives the membership material will join the club. nothing ​(Round to four decimal places as​ needed.)

b. Find the probability that a randomly chosen new student who joins the club after receiving the membership material is a woman. nothing ​(Round to four decimal places as​ needed.)

Answer 1

(a)

From the given data,the following Table is calculated:

	Men	Women	Total
Joined the club	0.35 X 0.08 = 0.028	0.65 X 0.11 = 0.0715	0.0995
Did not join the club	0.35 - 0.028 =0.322	0.5785	0.9005
Total	0.35	0.65	1.00

So,

the probability that a randomly chosen new student who receives the membership material will join the club. = 0.0995

So,

Answer is:

0.0995

(b)

P(Woman/ Joined the club) = P(Woman AND Joined the club)/ P(Joined the club)

                                     = 0.0715/ 0.0995

                                   = 0.7186

So,

Answer is:

0.7186