$A$ company produces $10,000$ items per day. On a particular day, $2500$ items were produced on machine $A$, $3500$ on machine $B$, and $4000$ on machine $C$. The probability that an item produced by machines $A, B, C$ is defective is $2 \%$, $3 \%$, and $5 \%$, respectively. If one item is selected at random from the output and is found to be defective, then the probability that it was produced by machine $C$ is:
- A$\frac{10}{71}$
- B$\frac{16}{71}$
- C$\frac{40}{71}$
- D$\frac{21}{71}$
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