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Class 12 Probability · Long Answer3 Marksindependence

Class 12 Maths · Probability · Long Answer #104

P and Q independently answer the same yes/no factual question. P is correct with probability 0.7 and Q with probability 0.8; an incorrect response is the opposite binary answer. Find P(they agree).

✅ Step-by-Step Solution

Final Answer: 31/50=62%
  1. Agreement has two disjoint possibilities: both give the true answer, or both give its binary opposite.
  2. By independence, P(both correct)=0.7·0.8=0.56.
  3. P(both wrong)=0.3·0.2=0.06. Hence P(agreement)=0.56+0.06=0.62.
  4. Thus they agree with probability 31/50, or 62%.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Agreement has two disjoint possibilities: both give the true answer, or both give its binary opposite.
  • [1 mark] By independence, P(both correct)=0.7·0.8=0.56.
  • [1 mark] P(both wrong)=0.3·0.2=0.06. Hence P(agreement)=0.56+0.06=0.62.
  • [0.5 marks] Thus they agree with probability 31/50, or 62%.

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