Please show work and write clearly.Thank you. #12. Customers who purchase a cert

Question

Please show work and write clearly.Thank you.

#12. Customers who purchase a certain make of car can order an engine in any of three sizes 40% have the smallest engine, 35% have the medium size one, and 25% have the largest Of cars with the smallest engine, 12% fail an ems ons test of those with the largest engine do. What is the probability that a randomly chosen car will fail an emissions test within two years? . Ofall cars sold, within two years of purchase, while 13% of those with the medium size and 14%

Explanation / Answer

P(smallest engine)=0.4

P(medium size)=0.35

P(largest)=0.25

P(fail test|smallest engine)=0.12

P(fail test|medium size)=0.13

P(fail test|largest)=0.14

P(fail test)=P(smallest engine)*P(fail test|smallest engine)+P(medium size)*P(fail test|medium size)+ P(largest)*P(fail test|largest) =0.4*0.12+0.35*0.13+0.25*0.14=0.1285

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