A certain company has two car assembly plants, A and B. Plant A produces twice a

Question

A certain company has two car assembly plants, A and B. Plant A produces twice as many cars as plant B. Plant A uses engines and transmissions from a subsidiary plant which produce 10% defective engines and 2% defective transmissions. Plant B uses engines and transmissions from another source where 8% of the engines and 4% of the transmissions are defective. Car transmissions and engines at each plant are installed independently. (a) What is the probability that a car chosen at random will have a good engine? (b) What is the probability that a car from plant A has defective engine, or a defective transmission, or both? Round up all your answers in four decimal places

Explanation / Answer

here probability from plant A =2/3

and from platn B =1/3

a) probability that a car chosen at random will have a good engine

=P(good engine) =P(plant A and good engine+Platn B and good engine) =(2/3)*0.1+(1/3)*(0.08)=0.0933

b)P(car from plant A has defective engine, or a defective transmission, or both) =P(plant A) -P(plant A and not defective engine not defective transmission) =(2/3)-(2/3)*(1-0.10)*(1-0.02)=0.0787

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