Question

In a certain college , 4% of men students and 1% of women students are taller than 1.8m . Further more , 60% of the students are women . If a student is selected at random and is found taller than 1.8m , What is the probability that the student is a women?

Answer 1

Among 1000 random students (say), there will be 600 women of whom 6 (1%) are 1.8 meters or more high. There will be 400 men of whom 16 (4%) are that high.

Since the selection was made at random from the student population and ended up with one of the taller people, the chances it is a woman are
6/(16 + 6) = 27% That is the fraction of "tall people" that are women.

There is a way to do this using Bayes' theorem of conditional probabilities, which I can never remember, but it should give the same result.

Answer 2

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