Question

There is a group of people consisting of 8 men and 4 women. Among these 12 people, there are 3 married couples (man-woman couples). If one man and one woman are selected at random, what is the probability that a married couple gets selected?

Answer 1

First, find the probability of choosing a married man among the 8 men.

Since there are 3 married couples, then there are 3 married men among the 8 men. Then, the probability of choosing a married man is:

`(3)/(8)`

On the other hand, only 1 among the group of 4 women is the wife of the previously chosen married man. The probability of picking the wife of that man is:

`(1)/(4)`

The probability of both events happening one after another is the product of the individual probabilities of choosing a married man and choosing that man's wife. Then, the probability that a married couple gets selected, is:

`(3)/(8)*(1)/(4)=(3)/(32)`

Therefore, the answer is: 3/32.