Question

A family has 2 children and the elder child is a girl. The probability that both children are girls is:

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

Hint:

Use conditional probability: reduce the sample space using the given condition.

Answer 1

The Correct Option is C

Possible combinations for 2 children: \[ \{ GG,\; GB,\; BG,\; BB \}. \] Given that the elder child is a girl, we only keep those cases where the elder is G: \[ \{ GG,\; GB \}. \] So, the favourable case is $GG$ out of $\{GG, GB\}$. \[ P(\text{both girls} | \text{elder is girl}) = \frac{1}{2}. \]