Question:

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

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Use conditional probability: reduce the sample space using the given condition.
  • $\frac{1}{4}$
  • $\frac{1}{8}$
  • $\frac{1}{2}$
  • $\frac{3}{4}$
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The Correct Option is C

Solution and Explanation

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 $\{GG, GB\}$. \[ P(\text{both girls} | \text{elder is girl}) = \frac{1}{2}. \]
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