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 probabilities of different cases when drawing balls from the bags.

### Step 1: Identify the contents of the bags
- **Bag 1**: 5 white balls, 3 black balls (Total = 8 balls)
- **Bag 2**: 3 white balls, 5 black balls (Total = 8 balls)

### Step 2: Determine the possible cases when drawing 2 balls from Bag 1
When we draw 2 balls from Bag 1, there are three possible cases:
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