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प्रश्न
A car manufacturing factory has two plants, X and Y. Plant X manufactures 70% of cars and plant Y manufactures 30%. 80% of the cars at plant X and 90% of the cars at plant Y are rated of standard quality. A car is chosen at random and is found to be of standard quality. What is the probability that it has come from plant X?
उत्तर
Let E be the event that the car is of standard quality.
Let B1 and B2 be the events that the car is manufactured in plants X and Y, respectively.
Now P(B1) = `70/100 = 7/10`
P(B2) = `30/100 = 3/10`
P(E|B1) = Probability that a standard quality car is manufactured in plant
= `80/100 = 8/10`
P(E|B2) = `90/100 = 9/10`
P(B1|E) = Probability that a standard quality car has come from plant X
= `("P"("B"_1) xx "P"("E"|"B"_2))/("P"("B"_1) * "P"("E"|"B"_1) + "P"("B"_2) * "P"("E"|"B"_2))`
= `(7/10 xx 8/10)/(7/10 xx 8/10 + 3/10 xx 9/10)`
= `56/83`
Hence the required probability is `56/83`.
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