A car producer stocks three types of tires: A, B, and C. Let P(A) = 0.40, P(B) = 0.15 and P(C) = 0.45. The percentage of defective tires is 2%, 1% and 5%, respectively. Someone picks a tire off the shelf at random and it is Brand A. If you want to know the probability that it is a defective tire (event D), which formula would you use? If you want to know the probability that it is a defective tire (event D), which formula would you use?
a.) P(A|D)= (P(D|A)P(A))/P(D)
b.) P(D|A) = (P(A|DP(D))/P(A)
c.) P(A|D)= (P(D|A)P(D))/P(A)
d.) P(D|A)= (P(A|D)P(A)/P(D)