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Probability, Statistics and Queueing

Five products are taken from a process with a defect rate of 20%. Whether each product is defective is independent of the others. Which of the following is closest to the probability that exactly one of the five is defective?

  1. A0.082
  2. B0.33
  3. C0.41
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Answer: C. 0.41

The number of defectives follows a binomial distribution with n = 5 and p = 0.2. The probability of exactly one defective is the 5C1 = 5 ways of choosing which of the five is defective multiplied by the probability 0.2 × 0.8⁴ = 0.08192 that this one is defective and the other four are good: 5 × 0.08192 = 0.4096 ≈ 0.41.

  • A. 0.2 × 0.8⁴ ≈ 0.082 is the probability that one particular product is the only defective one. There are 5 possibilities for which one it is.
  • B. 0.8⁵ ≈ 0.33 is the probability that all five are good.
  • C. Correct. 5C1 × 0.2 × 0.8⁴ = 0.4096 ≈ 0.41.
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