GATE | GATE CS 2010 | Question 26

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


Answer: (A)

Explanation:

A computer can be declared faulty in two cases
1) It is actually faulty and correctly declared so (p*q)
2) Not faulty and incorrectly declared (1-p)*(1-q).

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