Question

the theoretical probability of a couple having a baby girl is $\frac{1}{2}$. what is $p$(girl, girl, girl)?
$\frac{1}{8}$
$\frac{1}{6}$
$\frac{1}{3}$
$\frac{3}{8}$

Explanation:

Step1: Determine if events are independent

The gender of each baby is an independent event.

Step2: Use the formula for independent events

For independent events \(A\), \(B\), \(C\), \(P(A\cap B\cap C)=P(A)\times P(B)\times P(C)\). Here \(P(\text{girl})=\frac{1}{2}\) for each birth. So \(P(\text{girl},\text{girl},\text{girl})=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\).

Step3: Calculate the product

\(\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1\times1\times1}{2\times2\times2}=\frac{1}{8}\)

Answer:

\(\frac{1}{8}\) (the first option)