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Probability, Statistics and Queueing

A fab processed 500 wafers in a month, 100 of them in chamber 2. A total of 40 wafers failed, and 15 of these had been processed in chamber 2. Which of the following is the conditional probability that a wafer processed in chamber 2 fails?

  1. A0.15
  2. B0.20
  3. C0.375
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Answer: A. 0.15

The conditional probability P(fail | chamber 2) treats only the wafers processed in chamber 2 as the whole and finds the fraction of them that failed: 15 ÷ 100 = 0.15. Written as a formula, P(fail | chamber 2) = P(fail and chamber 2) ÷ P(chamber 2) = (15/500) ÷ (100/500) = 0.15. It is a different value from P(chamber 2 | fail) = 15/40 = 0.375, with the condition and the outcome swapped, so care is needed about which one is asked for.

  • A. Correct. 15 ÷ 100 = 0.15.
  • B. 100 ÷ 500 = 0.20 is the probability that a wafer is processed in chamber 2.
  • C. 15 ÷ 40 = 0.375 is the probability that a failed wafer was processed in chamber 2, with the condition and the outcome reversed.
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