A car manufacturing factory has two plants X and Y . Plant X manufactures 70 % of cars and plant Y manufactures 30 % of cars. 80 % of cars at plant X and 90 % of cars at plant Y are rated as standard quality. A car is chosen at random and is found to be standard quality. The probability that it has come from plant X is

Step-by-step solution

Let E= the event that the car is of standard quảlity. Let A₁= the event that the car is manufactured in plant X . and A₂= the event that the car is manufactured in plant Y . Now, P (A₁ )= 70 100 = 7 10 , P (A₂ )= 30 100 = 3 10 P ( E A₁ )= Probability that a standard quality car is manufactured in plant X= 80 100 = 8 10 P ( E A₂ )= Probability that a standard quality car is manu factured in blant Y= 90 100 = 9 10 P ( A₁ E )= Probability that a standard quality car has come from plant X aligned =& P (A₁ ) P ( E A₁ )