Question

A couple has $2$ children. What is the probability that both are girls if the older of the two is a girl ?

Short answer

$\frac{1}{2}$is the probability that both are girls if the older of the two is a girl.

Step-by-step solution

Step 1:Given Information

Given that a couple has $2$children.

Step 2:Explanation

Let$g$ signify a girl and $b$ indicate a boy.

Test space to the investigation is

$S=\{gg,gb,bg,bb\}$

Allow $A$ to signify the occasion that the two youngsters are girls.

$A=\left\{gg\right\}$

Allow $B$ to signify the occasion that the more established of the two is a girl.

$B=\{gg,gb\}$

The occasion that more established of the two is a girl and the two youngsters are girls.

$A\cap B=\left\{gg\right\}$

Step 3:Final Answer

The probability that both are girls if the older of the two is a girl is

$P(A\mid B)=\frac{P(A\cap B)}{P\left(B\right)}$

$=\frac{\left(\frac{1}{4}\right)}{\left(\frac{2}{4}\right)}$

$=\frac{1}{2}$