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.

Answer 1

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`