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…

In a bolt factory, machines $\displaystyle A, B$ and $\displaystyle C$ manufacture respectively $\displaystyle 20 \%, 30 \%$ and $\displaystyle 50 \%$ of the total bolts. Of their output $\displaystyle 3$, $\displaystyle 4$ and $\displaystyle 2$ 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 $\displaystyle C$ is