Question

Find the probability that when a couple has four ​children, at least one of them is a boy. ​(Assume that boys and girls are equally​ likely.)

Answer 1

The probability that at least, one of the four children the couple has is a boy is 0.8.

Explanation:

Given that boys and girls are equally likely, we want to find the probability of having at least, one boy, from four children..

Note that it is possible to have the following for 4 children:

1. 4 boys, 0 girls

2. 3 boys, 1 girl

3. 2 boys, 2 girls

4. 1 boy, 3 girls

5. 0 boys, 4 girls.

To have at least, one boy, out of the 5 options, only 4 is possible.

1. 4 boys, 0 girls.........YES

2. 3 boys, 1 girl ...........YES

3. 2 boys, 2 girls.........YES

4. 1 boy, 3 girls.............YES

5. 0 boys, 4 girls..........NO

The probability is therefore,

(Probability of event = 4) ÷ (Total possible outcome = 5)

P = 4/5 = 0.8