One bag contains 4 white and 5 black balls. Another bag contains 6 white and 7 black balls. A ball is transferred form first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is white.

A white ball can be drawn from the second bag in two mutually exclusive ways:

I. By transferring white ball from first bag to the second bag and then drawing a white ball from it.

II. By transferring a black ball from first bag to the second bag and then drawing a white ball from it.

Let E₁, E₂ and A be the events defined as follows:

E1 = a white ball is transferred from the first bag to the second bag

E2 = a black ball is transferred from the first bag to the second bag

A = a white ball id drawn from the second bag

Since the first bag contains 4 white and 5 black balls, we have

 P(E₁) = 4/9                   and P(E₂) = 5/9

If E₁ has already occurred, that is a white ball has already been transferred from first bag to the second bag, then the second bag contains 7 white and 7 black balls.

So, P(A/E₁) = 7/14

If E₂ has already occurred, that is a black ball has been transferred from first bag to the second bag, then the second bag contains 6 white and 8 black balls. So,