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Class 12 Probability · Very Long Answer5 Marksbayes_theorem

Class 12 Maths · Probability · Very Long Answer #121

Choose boxes I,II with equal probability. I contains3 red,6 black; II contains6 red,n black. Draw one uniform ball. Given red, P(box II)=3/5. Find n.

✅ Step-by-Step Solution

Final Answer: n=6
  1. Let E be a red draw. Both boxes have prior probability1/2.
  2. P(E|I)=1/3 and P(E|II)=6/(6+n), where n is a nonnegative integer.
  3. Bayes gives P(II|E)=[6/(6+n)]/[1/3+6/(6+n)]=18/(24+n).
  4. Set 18/(24+n)=3/5. Then90=72+3n, so n=6.
  5. Checking, 18/(24+6)=3/5. Thus box II has6 black balls.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Let E be a red draw. Both boxes have prior probability1/2.
  • [1 mark] P(E|I)=1/3 and P(E|II)=6/(6+n), where n is a nonnegative integer.
  • [1 mark] Bayes gives P(II|E)=[6/(6+n)]/[1/3+6/(6+n)]=18/(24+n).
  • [1 mark] Set 18/(24+n)=3/5. Then90=72+3n, so n=6.
  • [1 mark] Checking, 18/(24+6)=3/5. Thus box II has6 black balls.

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