In a factory that manufactures bolts, the first machine manufactures $70\%$ of the bolts and a second machine manufactures the remaining $30\%.$ The

percentage of defective bolts is $3\%$ and $5\%,$ respectively.

An employee picks a bolt off a shelf at random and it is from the first machine $($event A$).$

If you want to know the probability that it is a defective bolt $($event C$),$ which form of Bayes' rule would you use?

a$.)P(A|C)=\frac{P(C|A)P(A)}{P(C)}$

b$.)P(C|A)=\frac{P(A|C)P(C)}{P(A)}$

c$.)P(A|C)=\frac{P(A|C)P(A)}{P(C)}$

d$.)P(C|A)=\frac{P(A|C)P(A)}{P(C)}$