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Class 12 Probability · Very Long Answer5 Marksbayes_theorem

Class 12 Maths · Probability · Very Long Answer #78

In a college, 60% of students are girls. Of boys 4% exceed 1.75 m in height, and of girls 1% do. Given a uniform student exceeds 1.75 m, find P(girl).

✅ Step-by-Step Solution

Final Answer: 3/11
  1. Let E be the observed event. The mutually exclusive exhaustive cases are girl, boy. Their prior probabilities are P(girl)=3/5, P(boy)=2/5.
  2. The conditional observation probabilities are P(E|girl)=1/100, P(E|boy)=1/25.
  3. By total probability, P(E)=(3/5)(1/100) + (2/5)(1/25)=11/500.
  4. The requested joint probability with E is 3/500=3/500.
  5. By Bayes’ theorem, the requested posterior is 3/500 / (11/500) = 3/11.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Let E be the observed event. The mutually exclusive exhaustive cases are girl, boy. Their prior probabilities are P(girl)=3/5, P(boy)=2/5.
  • [1 mark] The conditional observation probabilities are P(E|girl)=1/100, P(E|boy)=1/25.
  • [1 mark] By total probability, P(E)=(3/5)(1/100) + (2/5)(1/25)=11/500.
  • [1 mark] The requested joint probability with E is 3/500=3/500.
  • [1 mark] By Bayes’ theorem, the requested posterior is 3/500 / (11/500) = 3/11.

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