Question

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 - p)q
• D. pq

Answer 1

The correct option is A pq + (1 - p) (1 - q)

Let A = {Computer declared faculty}, $E_1$ ={faculty computer},
$E_2$ = {Non faculty computer}
By total probability,
$P\left(A\right)=P\left(E_1\right).P\left(A/E_1\right)+P\left(E_2\right).P\left(A/E_2\right)$

$=p.q+(1-p)(1-q)$