Customers who purchase a certain make of car can order an engine in any of three sizes. Of all cars sold. 45% have the smallest engine, 35% have the medium-sized one, and 20% have the largest. Of cars with the smallest engine, 10% fail an emissions test within two years of purchase, while 12% of those with the medium size and 15% of those with the largest engine fail.

 (a) What is the probability that a randomly chosen car will fail an emissions test within two years?

  (b) A record for a failed emissions test is chosen at random. What is the probability that it is for a car with a small engine?