Answer to Question #167136 in Statistics and Probability for Angelo Agam

Question

A couple is planning to have three children.What is the probability that?

Answer 1

There are 8 possible arrangements of girls and boys. For example, GGB means the first two children are girls and the third child is a boy. All 8 arrangements are (approximately) equally alike.

The possible arrangements are:

GGG

GGB

GBG

GBB

BGG

BGB

BBG

BBB

Assume that the probability for aither B or G is $\frac{1}{2}$

So, the probability of any of these arrangements is:

$\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$