NECO 2023 · Paper 1 · Q42

One out of a thousand bulbs manufactured by a factory is found to be defective. If 2,000 bulbs were produced, find the probability that at least two bulbs are defective.

Worked solution (try it first)
  1. n=2000n = 2000 is large and p=0.001p = 0.001 is small, so use the Poisson approximation with λ=np=2\lambda = np = 2.
  2. "At least two" is 1 minus the chances of 0 and 1: P(X≥2)=1−e−2(1+2)P(X \ge 2) = 1 - e^{-2}(1 + 2)
    =1−3e−2= 1 - 3e^{-2}.
  3. 3e−2≈0.40603e^{-2} \approx 0.4060, so P(X≥2)≈0.5940P(X \ge 2) \approx 0.5940, option C.

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