Question

A survey questioned 1000 people regarding raising the legal drinking age from 18 to 21. Of the 590 who favored raising the age, 380 were female. Of the 410 who expressed opposition, 140 were female. (Enter your probabilities as fractions.) (a) What is the probability that a person selected at random is a female? (b) What is the probability that a person selected at random favors raising the age if the person is a woman??

Answer 1

(a) Total number of female = 380+140=520

So the probability that a person selected at random is a female=

(b) Let B= the event that a selected person is a woman.

Let A= the event that a person selected at random favors raising the age.

Then the probability that a person selected at random favors raising the age if the person is a woman =

Here Probability that a woman favors raising the age. =

P(B)=

So,    is the answer.

Here we have used Bayes theorem for probability for any two events A, B with P(B) greater than zero.