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+12 votes

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?

  1. $pq + (1 - p)(1 - q)$
  2. $(1 - q)p$
  3. $(1 - p)q$
  4. $pq$
asked in Probability by Boss (18.3k points)
edited by | 1.9k views

in this question two options ( B & C ) are same please correct it


3 Answers

+28 votes
Best answer

answer = option A

in image below the ticks shows those branch where the result is declared as faulty.

so required probability = sum of those two branches $= pq + (1-p)(1-q)$

answered by Boss (31.1k points)
edited by
nice amar
Can we say here that

A : Assembly is faulty

B : Test gives correct result

A and B are independent

Hence P(A) = P(A $\cap$ B) + P(A $\cap$ B') = [P(A)*P(B) + P(A)*P(B')]
+14 votes
I think a is the correct option ..

prob = pq + (1-p)(1-q)  // in words it means

(it is faulty)(machine detects correctly) + (it is not faulty)(machine detects incorrectly)
answered by Boss (14.4k points)
edited by
missed + between pq and (1 - p)(1 -q)
0 votes

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).


answered by Active (4.7k points)

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