Question

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? (Hint: Bayes' theorem)

a) 25
b) 3/5
c) 3/11
d) 1/100

Answer 1

To find the probability that a randomly selected student over six feet tall is a woman, we can use Bayes' theorem.

Step-by-step explanation:

To find the probability that a randomly selected student over six feet tall is a woman, we can use Bayes' theorem. Bayes' theorem states that the probability of an event A given event B is equal to the probability of event B given event A multiplied by the probability of event A, divided by the probability of event B.

Let's denote:

• A = the event that the student is a woman
• B = the event that the student is over six feet tall

We are given the following probabilities:

• P(A) = 2/5 (since the student population is divided in the ratio 3:2 in favor of women)
• P(B|A) = 1% (the probability of a woman being over six feet tall)
• P(B) = 4% (the probability of a man being over six feet tall)

Using Bayes' theorem, the probability that a randomly selected student over six feet tall is a woman is:

P(A|B) = (P(B|A) * P(A)) / P(B) = (0.01 * 2/5) / 0.04 = 0.005 / 0.04 = 0.125 = 12.5%

Therefore answer is c) 3/11.