Probability and conditional probability SAT question

Choice C is correct. It’s given that $29$ out of every $100$ beads that the machine produces have a defect. It follows that if the machine produces $k$ beads, then the number of beads that have a defect is $\frac{29}{100}k$, for some constant $k$. If a bead produced by the machine will be selected at random, the probability of selecting a bead that has a defect is given by the number of beads with a defect, $\frac{29}{100}k$, divided by the number of beads produced by the machine, $k$. Therefore, the probability of selecting a bead that has a defect is $\frac{\frac{29}{100}k}{k}$, or $\frac{29}{100}$.

Choice A is incorrect and may result from conceptual or computational errors.

Choice B is incorrect and may result from conceptual or computational errors.

Choice D is incorrect and may result from conceptual or computational errors.