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?
in this question two options ( B & C ) are same please correct it
Answer = option A
In image below the ticks show those branches where the result is declared as faulty.
So, required probability $=$ sum of probabilities of those two branches $= pq + (1-p)(1-q)$
A computer can be declared faulty only if--
it is faulty and testing process gives correct result(computer declared as faulty) OR it is not faulty and testing process gives incorrect result(that means computer declared as faulty).