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Class 12 Probability · Long Answer3 Marksbayes_theorem

Class 12 Maths · Probability · Long Answer #112

In a school,30% have full attendance and70% are irregular. Grade A rates are70% and10% respectively. Given a uniform student has grade A, find P(full attendance).

✅ Step-by-Step Solution

Final Answer: 3/4
  1. Let E be the observed event. The mutually exclusive exhaustive cases are full attendance, irregular. Their prior probabilities are P(full attendance)=3/10, P(irregular)=7/10.
  2. The conditional observation probabilities are P(E|full attendance)=7/10, P(E|irregular)=1/10. By total probability, P(E)=(3/10)(7/10) + (7/10)(1/10)=7/25.
  3. The requested joint probability with E is 21/100=21/100.
  4. By Bayes’ theorem, the requested posterior is 21/100 / (7/25) = 3/4.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Let E be the observed event. The mutually exclusive exhaustive cases are full attendance, irregular. Their prior probabilities are P(full attendance)=3/10, P(irregular)=7/10.
  • [1 mark] The conditional observation probabilities are P(E|full attendance)=7/10, P(E|irregular)=1/10. By total probability, P(E)=(3/10)(7/10) + (7/10)(1/10)=7/25.
  • [1 mark] The requested joint probability with E is 21/100=21/100.
  • [0.5 marks] By Bayes’ theorem, the requested posterior is 21/100 / (7/25) = 3/4.

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