Question

The probability of a boy or a girl being born is \( \frac{1}{2} \). For a family having only three children, what is the probability of having two girls and one boy?

• A. \( \frac{3}{8} \)
• B. \( \frac{1}{8} \)
• C. \( \frac{1}{4} \)
• D. \( \frac{1}{2} \)

Hint:

For probability problems involving multiple events, list all possible outcomes systematically. Identify favorable outcomes and divide by the total number of outcomes to find the probability.

Answer 1

The Correct Option is A

To calculate the probability of having two girls and one boy, we use the following steps: Step 1: Total number of outcomes. For a family with three children, each child can either be a boy (B) or a girl (G). Thus, the total number of outcomes is: \[ 2^3 = 8 \] The possible outcomes are: \( \{BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG\} \). Step 2: Favorable outcomes. We are interested in cases where there are two girls and one boy. These are: \[ \{BGG, GBG, GGB\} \] Thus, there are 3 favorable outcomes. Step 3: Probability calculation. The probability of a specific outcome is given by: \[ \text{Probability of each outcome} = \frac{1}{8} \] The probability of having two girls and one boy is: \[ \text{P(Two girls and one boy)} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{8} \] Conclusion.
The probability of having two girls and one boy is \( \frac{3}{8} \), making the correct answer \( \mathbf{(1)} \).