# Let the random variable X denote the number of girls in a five-child family. If the probability of a female birth is 0.5, what are the probabilities of having 0, 1, 2, 3, 4, and 5 girls?

##### 1 Answer

See below:

#### Explanation:

The probability of having a girl is given as

The last thing to look at is the number of ways we can achieve any given result. For instance, there is only 1 way to have 0 girls (and the same goes for 5 girls), but there are 5 different ways we can have 1 girl (and the same goes for 4 girls). This is a combinations question, with:

Boiling it all down, we end up with:

0 girls

1 girl

2 girls

3 girls

4 girls

5 girls

Notice that if we add all of these up, we get 1 (or the sum total of all probabilities):