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CA Foundation · Quantitative Aptitude · Theoretical Distributions

Defects in a roll of cloth produced by a Ludhiana mill follow a Poisson distribution. It is known that P(X=1) = P(X=2) for the number of defects per roll. What is the probability that a roll has no defects? (Use e^-2 = 0.1353)

The probability of no defects is 0.1353. Setting P(1) equal to P(2) gives m = m²/2, so the mean m is 2. Then P(0) = e^-2 = 0.1353. The value 0.2707 is the probability of one defect, not zero.

  1. A0.2707
  2. B0.0677
  3. C0.1353Correct
  4. D0.3679

Explanation

P(1)=e^-m·m and P(2)=e^-m·m²/2. Equating gives m = m²/2, so m = 2 (m=0 is rejected). Then P(0) = e^-2 = 0.1353. Option A is P(1) = P(2) = 0.2707, which is a wrong x. Option D uses m = 1.

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