Question

2. Customers who purchase a certain model of car can order an engine in any of three sizes. Of all cars of this type sold, 45% have a small engine, 35% have a medium-sized engine, and 20% have a large engine. Of cars with the small engine, 10% fail an emission test within two years of purchase, while 12% of those with the medium size and 15% of those with the large engine fail. If a randomly chosen car of this model fails an emission test within two years, what is the probability it is a car with a small engine

Answer 1

Answer: 0.1397 ; 0.385

Explanation:

Given the following :

Small engine population = 45% ; 10% fail

Medium engine population = 35% ; 12% fail

Large engine population = 20% ; 15% fail

Probability that a randomly chosen car fails emission test :

P(failure) = Σ(population % * failure %)

P(failure) = (45%*10%) + (35%*12%) + (20%*15%)

P(failure) = 0.045 + 0.042 + 0.03 = 0.117

B) what is the probability it is a car with a small engine

P = small engine cars with emission failure / total emission failure

= (0.45 × 0.1) / 0.117 = 0.045 / 0.117 = 0.3846

= 0.385