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Class 12 Probability · Long Answer3 Marksbayes_theorem

Class 12 Maths · Probability · Long Answer #59

A,B,C are selected as manager with probabilities in ratio 1:2:4. Their respective probabilities of introducing an improvement are 0.8,0.5,0.3. Given no improvement, find P(C was appointed).

✅ Step-by-Step Solution

Final Answer: 7/10
  1. Let E be the observed event. The mutually exclusive exhaustive cases are A, B, C. Their prior probabilities are P(A)=1/7, P(B)=2/7, P(C)=4/7.
  2. The conditional observation probabilities are P(E|A)=1/5, P(E|B)=1/2, P(E|C)=7/10. By total probability, P(E)=(1/7)(1/5) + (2/7)(1/2) + (4/7)(7/10)=4/7.
  3. The requested joint probability with E is 2/5=2/5.
  4. By Bayes’ theorem, the requested posterior is 2/5 / (4/7) = 7/10.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Let E be the observed event. The mutually exclusive exhaustive cases are A, B, C. Their prior probabilities are P(A)=1/7, P(B)=2/7, P(C)=4/7.
  • [1 mark] The conditional observation probabilities are P(E|A)=1/5, P(E|B)=1/2, P(E|C)=7/10. By total probability, P(E)=(1/7)(1/5) + (2/7)(1/2) + (4/7)(7/10)=4/7.
  • [1 mark] The requested joint probability with E is 2/5=2/5.
  • [0.5 marks] By Bayes’ theorem, the requested posterior is 2/5 / (4/7) = 7/10.

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