Consider a company that 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 a probability of q. What is the probability of a computer being declared faulty?
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pq + (1 − p) (1 − q)
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(1 − q)p
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(1 − p) q
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pq
A
Correct answer
Explanation
A computer is declared faulty in two cases: (1) It is actually faulty AND the test correctly identifies it: probability = p × q. (2) It is NOT faulty BUT the test wrongly declares it faulty: probability = (1-p) × (1-q). These are mutually exclusive events, so we add them: P(declared faulty) = pq + (1-p)(1-q). This is Option A. Option D (pq) only counts true positives, missing false positives. Options B and C only capture one scenario each.