In a bolt factory, machines A, B and C manufacture respectively, 25%, 35% and 40% of the total bolts. Of their output 5, 4, and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found to be defective, what is the probability that it is manufactured by the machine B?

Let E₁, E₂, E₃ and A be the events defined as follows:

E₁ = the bolt is manufactured by machine A,            

E₂ = the bolt is manufactured by machine B,

E₃ = the bolt is manufactured by machine C.

A = the bolt is defective.

Then, P(E₁) = Probability that the bolt drawn is manufactured by machine A = 25/100

P(E₂) = Probability that the bolt drawn is manufactured by machine B = 35/100

P(E₃) = Probability that the bolt drawn manufactured by machine C = 40/100