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Class 12 Probability · Very Long Answer5 Marksbayes_theorem

Class 12 Maths · Probability · Very Long Answer #81

Roll a fair die. On 1 or 2, toss a fair coin independently three times; on 3,4,5,6 toss it once. Given exactly one tail was obtained, find P(die was 3,4,5,6).

✅ Step-by-Step Solution

Final Answer: 8/11
  1. Let E be the observed event. The mutually exclusive exhaustive cases are die 1,2, die 3,4,5,6. Their prior probabilities are P(die 1,2)=1/3, P(die 3,4,5,6)=2/3.
  2. The conditional observation probabilities are P(E|die 1,2)=3/8, P(E|die 3,4,5,6)=1/2.
  3. By total probability, P(E)=(1/3)(3/8) + (2/3)(1/2)=11/24.
  4. The requested joint probability with E is 1/3=1/3.
  5. By Bayes’ theorem, the requested posterior is 1/3 / (11/24) = 8/11.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Let E be the observed event. The mutually exclusive exhaustive cases are die 1,2, die 3,4,5,6. Their prior probabilities are P(die 1,2)=1/3, P(die 3,4,5,6)=2/3.
  • [1 mark] The conditional observation probabilities are P(E|die 1,2)=3/8, P(E|die 3,4,5,6)=1/2.
  • [1 mark] By total probability, P(E)=(1/3)(3/8) + (2/3)(1/2)=11/24.
  • [1 mark] The requested joint probability with E is 1/3=1/3.
  • [1 mark] By Bayes’ theorem, the requested posterior is 1/3 / (11/24) = 8/11.

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