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CBSE Class 12 Mathematics 2026 Main Paper 65/3/1 · Q313 Marksindependent_trials

CBSE Class 12 Mathematics 2026 Main Paper 65/3/1 · Question 31 (Probability)

Three patients undergo independent surgeries, each with 90% success probability. Find the probabilities of (i) exactly one success and (ii) at most two successes.

✅ Step-by-Step Solution

Final Answer: (i) 27/1000. (ii) 271/1000.
  1. For each surgery, P(success)=0.9 and P(failure)=0.1.
  2. Exactly one success has three possible positions, giving 3·0.9·0.1²=27/1000.
  3. At most two is the complement of all three succeeding, giving 1−0.9³=271/1000.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] For each surgery, P(success)=0.9 and P(failure)=0.1.
  • [2 marks] Exactly one success has three possible positions, giving 3·0.9·0.1²=27/1000.
  • [0.5 marks] At most two is the complement of all three succeeding, giving 1−0.9³=271/1000.

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/3/1

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