A computer producing factory has only two plants T 1 and T 2 . Plant T 1 produces 20 % and plant T 2 produces 80 % of the total computers produced. 7 % of computers produced in the factory turn out to be defective. It is known that, P ( computer   turns   out   to   be   defective   given   that   it   is   produced   in   plant   T 1 ) = 10   P (

Step-by-step solution

P T 1 = 20 100 P T 2 = 80 100 Let, P D T 2 = x (where, D represents defective units) P D T 1 = 10 x P D = 7 100 (given) P T 1   P D T 1 + P T 2   P D T 2 = 7 100 20 100 × 10 x + 80 100 × x = 7 100 x = 1 40 P D T 2 = 1 40   ⇒ P D - T 2 = 39 40 =  Probability of not defective, given that it is produced in plant T 2 P D T 1 = 10 40   ⇒     P D - T 1 = 30 40 Now using Bayes' theorem Probability of computer from T 2 given that it is not defective : P T 2 D - =