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प्रश्न
Refer to Question 41 above. If a white ball is selected, what is the probability that it came from Bag 2
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उत्तर
We will use here Bayes’ Theorem
`"P"("E"_2/"F") = ("P"("E"_2)*"P"("F"/"E"_2))/("P"("E"_1) * "P"("F"/"E"_1) + "P"("E"_2) * "P"("F"/"E"_2) + "P"("E"_3) * "p"("F"/"E"_3))`
= `(2/6*1/3)/(1/6*0 + 2/6*1/3 + 3/6*1)`
= `(2/18)/(2/18 + 3/6)`
= `2/11`
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(Activity):
Mr. X goes to office by Auto, Car, and train. The probabilities him travelling by these modes are `2/7, 3/7, 2/7` respectively. The chances of him being late to the office are `1/2, 1/4, 1/4` respectively by Auto, Car, and train. On one particular day, he was late to the office. Find the probability that he travelled by car.
Solution: Let A, C and T be the events that Mr. X goes to office by Auto, Car and Train respectively. Let L be event that he is late.
Given that P(A) = `square`, P(C) = `square`
P(T) = `square`
P(L/A) = `1/2`, P(L/C) = `square` P(L/T) = `1/4`
P(L) = P(A ∩ L) + P(C ∩ L) + P(T ∩ L)
`="P"("A")*"P"("L"//"A") + "P"("C")*"P"("L"//"C") + "P"("T")*"P"("L"//"T")`
`= square * square + square * square + square * square`
`= square + square + square`
`= square`
`"P"("C"//"L") = ("P"("L" ∩ "C"))/("P"("L"))`
= `("P"("C") * "P"("L"//"C"))/("P"("L"))`
`= (square * square)/square`
`= square`
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