Question

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

Explanation:

Step1: Identify the probability of one girl

The probability of having a baby girl is given as $\frac{1}{2}$.

Step2: Use the multiplication rule for independent events

Since the gender of each baby is an independent event, the probability of having three girls in a row is the product of the probabilities of having a girl each time. So we calculate $\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}$.

Step3: Calculate the product

$\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1 \times 1}{2 \times 2 \times 2} = \frac{1}{8}$.

Answer:

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