Two families, each with 2 children, boy/girl equally likely.

Question

Two families, each with 2 children, boy/girl equally likely. Find the conditional probability all children are girls given at least two are girls.

Accepted Answer

$P(\text{all 4 girls}) = \left(\dfrac12\right)^4=\dfrac{1}{16}$. $P(\text{at least 2 girls out of 4}) = 1-{}^4C_0\left(\dfrac12\right)^4-{}^4C_1\left(\dfrac12\right)^4=\dfrac{11}{16}$.

$$P = \frac{1/16}{11/16}=\frac{1}{11}$$

Solutions · 1