Question

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

Explanation:

Step1: Identify independent events

Each birth is an independent event, so we multiply the probabilities.
Probability of a girl, \( P(\text{girl}) = \frac{1}{2} \)

Step2: Calculate the probability of three girls

For three independent events (three girls), we use the multiplication rule: \( P(\text{girl, girl, girl}) = P(\text{girl}) \times P(\text{girl}) \times P(\text{girl}) \)
Substitute \( P(\text{girl}) = \frac{1}{2} \):
\( P(\text{girl, girl, girl}) = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \)
\( = \frac{1 \times 1 \times 1}{2 \times 2 \times 2} \)
\( = \frac{1}{8} \)

Answer:

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