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Question
A bag contains 6 red and 5 blue balls and another bag contains 5 red and 8 blue balls. A ball is drawn from the first bag and without noticing its colour is placed in the second bag. If a ball is drawn from the second bag, then find the probability that the drawn ball is red in colour.
Solution
Let P(A) = Probability of getting a red ball from the second bag
P(E1) = Probability of getting a red ball from the first bag
P(E2) = Probability of getting a blue ball from the first bag
∴ P(E1) = `6/11`
⇒ `"P"("A"/"E"_1) = 6/14`
and P(E2) = `5/11`
⇒ `"P"("A"/"E"_2) = 5/14`
∴ P(A) = `"P"("E"_1) xx "P"("A"/"E"_1) + "P"("E"_2) xx "P"("A"/"E"_2)`
⇒ P(A) = `6/11 xx 6/14 + 5/11 xx 5/14`
∴ P(A) = `61/154`
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