GATE2010 q26 Revision as of 14:40, 29 June 2014 by Arjun Suresh (talk | contribs) (diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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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