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At a certain university, 4% of men are over 6 feet tall and 1% of women are over 6 feet tall. The total student population is divided in the ratio 3:2 in favour of women. If a student is selected at random from among all those over six feet tall, what is the probability that the student is a woman?

At a certain university, 4% of men are over 6 feet tall and 1% of women are over 6 feet tall. The total student population is divided in the ratio 3:2 in favour of women. If a student is selected at random from among all those over six feet tall, what is the probability that the student is a woman? Correct Answer 3⁄11

Let M be the event that student is male and F be the event that the student is female. Let T be the event that student is taller than 6 ft. P(M) = 2⁄5 P(F) = 3⁄5 P(T|M) = 4⁄100 P(T|F) = 1⁄100 P(F│T) = (P(T│F) * P(F))/(P(T│F) * P(F) + P(T│M) * P(M)) = ((1/100) * (3/5))/((1/100) * (3/5) + (4/100) * (2/5) ) = 3⁄11.

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