3. A certain company has two car assembly plants, A and B. Plant A produces twic

Question

3. 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 subsid- ary plant which produces 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 a defective engine, or a defective transmission, or both? What is the probability that a car which has a good transmission and a defective engine was assembled at plant B? c)

Explanation / Answer

here let probability of car is from plant A =P(A) =2/3

and that from plant B =P(B)=1/3

probability of defective engine given plant A =P(DE|A) =0.10

probability of defective transmission given plant A =P(DT|A) =0.02

probability of defective engine given plant B =P(DE|B) =0.08

probability of defective transmission given plant B =P(DTB) =0.04

a)

probability of car to have good engine P(GE) =P(A)*P(GE|A)+P(B)*P(GE|B) =(2/3)*(1-0.10)+(1/3)*(1-0.08)=0.9067

b)

probability that a car from plant A defective engine or transmission or Both =P(DE|A)+P(DT|A)-P(DE and DT|A)   

=0.10+0.02-0.10*0.02=0.118

c)probability of car having good transmission and defective engine P(GE & DT)

=P(A)*P(GT &DE|A)+P(B)*P(GT &DE|B)

=(2/3)*(1-0.02)*0.1+(1/3)*(1-0.04)*0.08=0.0909

therefore probability of car from plant B given car having good transmission and defective engine

=P(B)*P(GT &DE|B) /P(GT and DE) =(1/3)*(1-0.04)*0.08/0.0909 =0.2816

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