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A car manufacturing factory has two plants X and Y. Plant X manufactures 70% of tl1e cars and plant Y manufactures 30%. At plant X, 80% of the cars are rated of standard quality and at plant Y, 90% are rated of standard quality. A car is picked up at random and is found to be of standard quality. Find the probability that it has come from plantX.

Answer»

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SOLUTION :LET `E_1 and E_2` be the EVENTS that the car is manugactured by PLANT X and Y respectively. Let E be the event that the car is of standard quality. Then,
`P(E_1)=70/100=7/10,P(E_2)=30/100=3/10`,
`P(E//E_1)=80/100=4/5,P(E//E_2)=90/100=9/10`
`:. P(E_1//E)=(P(E_1)xxP(E//E_1))/(P(E_1)xxP(E//E_1)+P(E_2)xxP(E//E_2))`
`=((7/10xx4/5))/((7/10xx4/5)+(3/10xx9/10))=56/83`.


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