Question

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 engines, 35% have the medium engines, and 20% have the largest ones. 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% with the largest engine fail. 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?

Answer 1

0.385

Explanation:

45% have the smallest engines, 35% have the medium engines, and 20% have the largest ones.

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% with the largest engine fail.

True Percentage of small engine cars that will fail the emission test = 0.10 × 0.45 = 0.045 = 4.5%

True Percentage of medium engine cars that will fail the emission test = 0.12 × 0.35 = 0.042 = 4.2%

True Percentage of large engine cars that will fail the emission test = 0.15 × 0.20 = 0.030 = 3.0%

Total percentage of engines that will fail the emission test = 4.5% + 4.2% + 3.0% = 11.7%

Probability that a car that failed the emission test, picked at random is a small engine car = (4.5/11.7) = 0.385