In a bolt factory, machines A , B and C manufacture respectively 20 % , 30 % and 50 % of the total bolts. Of their output 3 , 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found the defective then the probability that it is manufactured by the machine C is

Step-by-step solution

Let X ≡ Event that product is defective, then P X A = 3 100 P X B = 4 100 P X C = 2 100 Now, P C X = P C P X C P A P X A + P B P X B + P C P X C ⇒ P C X = 50 100 × 2 100 20 100 × 3 100 + 30 100 × 4 100 + 50 100 × 2 100 ⇒ P C X = 100 60 + 120 + 100 ⇒ P C X = 5 14 Hence this is the correct option.