Question

A bag contains 4 white and 5 black balls. Another bag contains 9 white and 7 black balls. A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag. Find the probability that the ball drawn is white.

Answer 1

Let W₁ and W₂ be two bags containing (4W, 5B) and (9W, 7B) balls respectively.

Let E₁ be the event that the transferred ball from the bag W₁ to W₂ is white and E₂ the event that the transferred ball is black.

And E be the event that the ball drawn from the second bag is white.

∴ `"P"("E"_1/"E"_1) = 10/17`

`"P"("E"/"E"_2) = 9/17`

`"P"("E"_1) = 4/9` and `"P"("E"_2) = 5/9`

∴ P(E) = `"P"("E"_1)."P"("E"/"E"_1) + "P"("E"_2)."P"("E"/"E"_2)`

= `4/9 xx 10/17 + 5/9 xx 9/17`

= `40/153 + 45/153`

= `85/153`

= `5/9`

Hence, the required probability is `5/9`.