Discussion
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 ?
Answer: A
The probability is \(pq + (1-p)(1-q)\).
A computer is declared faulty in two ways:
- it is faulty (probability p) and the test is correct (probability q): \(pq\);
- it is good (probability 1 - p) and the test is wrong (probability 1 - q): \((1-p)(1-q)\).
Adding the two disjoint cases gives the answer. \(pq\) alone counts only the correctly detected faults, while \((1-q)p\) and \((1-p)q\) are the cases where a faulty machine passes or a good machine is correctly passed.
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