SOLUTION: Enrollment statistics at a certain college show that 55% of all students are men, 18% of the student body consists of women majoring in business, and 40% of all students major in b

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Question 369654: Enrollment statistics at a certain college show that 55% of all students are men, 18% of the student body consists of women majoring in business, and 40% of all students major in business. A student is selected at random.
Find the conditional probability that the person majors in business if we are certain the person is a woman.
I've got P(men) = 55 and P(women majoring in business) = 18, but the 40% I do not know what to do. I tried Venn diagram and:
P(M U W) = P(M) + P(W) - P(M n W) I still cannot get answer..




Found 2 solutions by edjones, jrfrunner:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Make a Venn diagram of Women and Bussiness majors.
P=P(WnB)|P(W)(.18/.45=.40 the conditional probability that the person majors in business if we are certain the person is a woman.
.
Ed

Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
given
P(Man)=0.55, P(Woman AND Business)=0.18, P(Business)=0.40
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from this P(Woman)=1-P(man)=1-0.55=0.45
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Using the probability rule P(A/B)=P(A and B)/P(B)
Want
P(Business given Woman)=P(Woman AND Business)/P(Woman)=0.18/0.45=0.40