We want to know how likely the event is that the two oldest children in a family with three children are girls. To figure this out, we will list every way in which the three children could be born. We will write

B

for boys and

G

for girls. Let's write an example!

GG B

This example indicates that the oldest child is a girl, the second child is a girl, and the youngest child is a boy. This one of the cases that would fit the given scenario! Now, let's list all the ways in which the three children could be born.

BBB, BB G, B G B, B GG, G BB, G B G, GG B, GGG

To determine the probability that the two oldest children in a family with three children are girls, we will divide the ways in which the two oldest children are girls by all the ways in which the three children could be born. We can see that there are

2

ways in which the two oldest children are girls and

8

ways in total.

P (GG ?) = \frac{ways two oldest children are girls}{total ways}

SubstituteValues

Substitute values

P (GG ?) = \frac{2}{8}

ReduceFrac

$\frac{a}{b} = \frac{a / 2}{b / 2}$

P (GG ?) = \frac{1}{4}

The probability that the family has two girls as their first two children is

\frac{1}{4} .

Because this is less than half, the event that the two oldest children in a family with three children are girls is unlikely.

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