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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?

(A) pq + (1 - p)(1 - q)

(B) (1 - q)p

(C) <(1 - q)p

(D) pq

Solution by Happy Mittal

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.




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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?

(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.




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