A certain manufacturer produces cars at two factories labeled A and B. 10% of the cars produced at factory A are found to be defective, while 5% of the cars produced at factory B are defective. If factory A produces 100,000 cars per year and factory B produces 50,000 cars per year, compute the following:
a. The probability of purchasing a defective car from the manufacturer
b. If a car purchased from the manufacturer is defective, what is the probability that it came from factory A?