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
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.
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
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.
GATECSE