Question

There are two bags, one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls. A die is thrown. If it shows up 1 or 3, a ball is taken from the Ist bag; but it shows up any other number, a ball is chosen from the second bag. Find the probability of choosing a black ball.

Answer 1

Let E₁ be the event of selecting Bag I

And E₂ be the event of selecting Bag II

Let E₃ be the event that black ball is selected

∴ P(E₁) = `2/6 = 1/3` and P(E₂) = `1 - 1/3 = 2/3`

`"P"("E"_3/"E"_1) = 3/7` and `"P"("E"_3/"E"_2) = 4/7`

∴ P(E₃) = `"P"("E"_1) * "P"("E"_3/"E"_1) + "P"("E"_2) * "P"("E"_3/"E"_2)`

= `1/3*3/7 + 2/3*4/7`

= `(3 + 8)/21`

= `11/21`

Hence, the required probability is `11/21`.