Class 12 Probability · Long Answer3 Marksconditional_probability
Class 12 Maths · Probability · Long Answer #55
Uniformly select a committee of 4 from 7 boys and 4 girls. Given at least one girl is selected, find P(exactly two boys).
✅ Step-by-Step Solution
Final Answer: 126/295
- Conditioning restricts to committees with at least one girl. All such committees remain equally likely.
- The restricted count is C(11,4)−C(7,4)=330−35=295.
- Exactly two boys requires two girls: C(7,2)C(4,2)=21·6=126 committees, all in the restricted space.
- Thus P(exactly two boys|at least one girl)=126/295.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Conditioning restricts to committees with at least one girl. All such committees remain equally likely.
- [1 mark] The restricted count is C(11,4)−C(7,4)=330−35=295.
- [1 mark] Exactly two boys requires two girls: C(7,2)C(4,2)=21·6=126 committees, all in the restricted space.
- [0.5 marks] Thus P(exactly two boys|at least one girl)=126/295.
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