a) 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. Among the 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. Calculate the probability that a randomly chosen car will fail an emissions test within two years.

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