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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?

1. pq + (1 - p)(1 - q)
2. (1 - q)p
3. (1 - q)p
4. pq
edited | 1.3k views

in image below the ticks shows those branch where the result is declared as faulty.

so required probability = sum of those two branches $= pq + (1-p)(1-q)$

edited
I think a is the correct option ..

prob = pq + (1-p)(1-q)  // in words it means

(it is faulty)(machine detects correctly) + (it is not faulty)(machine detects incorrectly)
edited
missed + between pq and (1 - p)(1 -q)