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A company assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with probability q. What is the probability of a computer being declared faulty?

1. pq + (1-p)(1-q)
2. (1-q)p
3. (1-p)q
4. pq

Correct answer: pq + (1-p)(1-q)

Solution

A computer is declared faulty in two cases: it is faulty and the test correctly identifies it, or it is not faulty and the test incorrectly labels it faulty. These probabilities are pq and (1-p)(1-q), respectively. Adding them gives pq + (1-p)(1-q).

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