Question:
If it is known that a woman has two children and she has at least one girl child, then the probability that both children are girls is
If it is known that a woman has two children and she has at least one girl child, then the probability that both children are girls is
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Whenever a condition such as ``at least one'' is given, first reduce the sample space accordingly and then calculate probability within the reduced sample space.
Updated On: Jun 10, 2026
- \(\frac13\)
- \(\frac14\)
- \(\frac12\)
- \(\frac23\)
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The Correct Option is A
Solution and Explanation
Concept:
This is a conditional probability problem.
The sample space for two children is
\[
\{BB,BG,GB,GG\}.
\]
Assuming each outcome is equally likely.
Step 1: Apply the given condition The condition states that at least one child is a girl. Therefore \(BB\) is excluded. The reduced sample space becomes \[ \{BG,GB,GG\}. \] Total favourable possibilities after conditioning \[ =3. \]
Step 2: Count favourable outcomes For both children to be girls, \[ GG \] is the only favourable outcome. Number of favourable cases \[ =1. \]
Step 3: Compute probability \[ P(\text{both girls}\mid \text{at least one girl}) = \frac{1}{3}. \] Hence, \[ \boxed{\frac13}. \]
Step 1: Apply the given condition The condition states that at least one child is a girl. Therefore \(BB\) is excluded. The reduced sample space becomes \[ \{BG,GB,GG\}. \] Total favourable possibilities after conditioning \[ =3. \]
Step 2: Count favourable outcomes For both children to be girls, \[ GG \] is the only favourable outcome. Number of favourable cases \[ =1. \]
Step 3: Compute probability \[ P(\text{both girls}\mid \text{at least one girl}) = \frac{1}{3}. \] Hence, \[ \boxed{\frac13}. \]
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