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Class 12 Probability · Long Answer3 Markstotal_probability

Class 12 Maths · Probability · Long Answer #56

Bag A has 4 black and 6 red balls; bag B has 7 black and 3 red. A fair die selects A on 1 or 2, otherwise B. Draw 2 uniformly without replacement. Find P(one red and one black).

✅ Step-by-Step Solution

Final Answer: 22/45
  1. The bag probabilities are P(A)=1/3 and P(B)=2/3.
  2. Given A, the mixed-pair probability is C(6,1)C(4,1)/C(10,2)=24/45. Given B it is 3·7/45=21/45.
  3. By total probability, P(mixed pair)=(1/3)(24/45)+(2/3)(21/45)=8/45+14/45.
  4. The required probability is 22/45.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] The bag probabilities are P(A)=1/3 and P(B)=2/3.
  • [1 mark] Given A, the mixed-pair probability is C(6,1)C(4,1)/C(10,2)=24/45. Given B it is 3·7/45=21/45.
  • [1 mark] By total probability, P(mixed pair)=(1/3)(24/45)+(2/3)(21/45)=8/45+14/45.
  • [0.5 marks] The required probability is 22/45.

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