Question:
A family has 2 children and the elder child is a girl. The probability that both children are girls is:
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.
Updated On: Jul 1, 2025
- $\frac{1}{4}$
- $\frac{1}{8}$
- $\frac{1}{2}$
- $\frac{3}{4}$
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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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