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 $2 \%$ are respectively defective bolts. $A$ bolt is drawn at random from the product. If the bolt drawn is found to be defective,then the probability that it is manufactured by the machine $C$ is
- A$\frac{2}{7}$
- B$\frac{9}{28}$
- C$\frac{5}{14}$
- D$\frac{3}{7}$
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