In a bolt factory, machines X, Y, Z manufacture bolts that are respectively 25%, 35% and 40% of the factory's total output. The machines X, Y, Z respectively produce 2%, 4% and 5% defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X?

Options

A. `(5)/(39)`
B. `(11)/(39)`
C. `(20)/(39)`
D. `(34)/(39)`

Answer

A

Explanation

Required probability.
` = (25 xx 2)/(25 xx 2 + 35 xx 4 + 40 xx5) = (5)/(39)`.