Question

Consider the composition of a three-child family. Assume that a girl is as likely as a boy at each birth. What is the probability that there is one boy and two girls in the family?

Answer 1

I believe the answer is 3/8.

Answer 2

3/8 is correct.

It can be calculated as follows:
A. By enumeration
GGG
GGB
GBG
BGG
BBG
BGB
GBB
BBB
So out of the 8 possible combinations, there there are 3 (second to fourth) that have two girls and 1 boy.

B. By enumeration, useful for large numbers.
number of possible combinations = 2³
Note: B or G are the 2 possible outcomes, and there are 3 children.
Number of possible combinations of 2 girls and 1 boy (out of 3 children
= 3!/(2!1!)
= 3*2*1/(2*1 * 1)
= 3

So probability = 3/8