There are two bags. The first bag contains 5 white and 3 black balls and the second bag contains 3 white and 5 black balls. Two balls are drawn at random from the first bag and are put into the second bag without noticing their colours. Then two balls are drawn from the second bag. Find the probability that the balls are white and black.

Explanation

To solve the problem step by step, we will calculate the probability of drawing one white and one black ball from the second bag after transferring two balls from the first bag to the second bag. We will consider all possible cases for the colors of the balls drawn from the first bag.

### Step 1: Define the initial conditions
- **First Bag**: 5 white balls, 3 black balls
- **Second Bag**: 3 white balls, 5 black balls

### Step 2: Calculate the total number of ways to draw 2 balls from the first bag
The total number of balls in the first bag is \(5 + 3 = 8\). The number of ways to choose 2 balls from 8 is given by:
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