Binomial Probability of Defective Items
Mediumprobabilitybinomial
A process produces defective items independently 20% of the time. In a sample of 5 items, the probability that exactly 2 are defective is most nearly:
- A0.02
- B0.08
- C0.21
- D0.26
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Answer: C. 0.21
This is a binomial probability: P(X = 2) = C(5,2)p²(1−p)³ = 10(0.2)²(0.8)³ = 10(0.04)(0.512) ≈ 0.21. The binomial coefficient C(5,2) = 10 counts the ten distinct positions the two defectives can occupy; dropping it gives 0.02 and is the most common error here.
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