Question

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

Explanation:

Step1: Identify the probability of one girl

The probability of having a girl is $P(\text{girl}) = \frac{1}{2}$.

Step2: Use the multiplication rule for independent events

Since the gender of each baby is an independent event, the probability of having three girls is the product of the probabilities of having a girl each time. So we calculate $P(\text{girl, girl, girl}) = P(\text{girl}) \times P(\text{girl}) \times P(\text{girl})$.
Substitute $P(\text{girl}) = \frac{1}{2}$ into the formula: $\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$.

Answer:

$\frac{1}{8}$ (corresponding to the option with $\frac{1}{8}$)