Consider a company that assembles computers. The probability of a faulty…
20102025
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?
- A.
\(pq + (1 - p) (1 - q)\) - B.
\((1 - q) p\) - C.
\( (1 - p) q\) - D.
\(pq\)
Attempted by 58 students.
Show answer & explanation
Correct answer: A
Idea: Use the law of total probability by conditioning on whether the computer is actually faulty.
Case 1 – actually faulty: This occurs with probability p. The test gives the correct result (declares it faulty) with probability q, so contribution = p·q.
Case 2 – actually good: This occurs with probability 1−p. The test gives an incorrect result (declares it faulty) with probability 1−q, so contribution = (1−p)·(1−q).
Add the two mutually exclusive contributions to get the total probability of being declared faulty:
Final result: p·q + (1−p)·(1−q).
Optional check: If p = 0 (no actual faults) the expression becomes 1−q (the false positive rate), and if p = 1 (all are faulty) it becomes q (the true positive rate), which matches expectations.