View source for GATE2010 q26 ← GATE2010 q26

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 - q)p

(D) pq

Solution by Happy Mittal[edit]

P(declared faulty) 
= P(actually faulty)*P(declared faulty|actually faulty) +  P(not faulty)*P(declared faulty|not faulty) 
= p*q + (1-p)*(1-q)

So, option (A) is correct.