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 fair die is cast, if the face `1` or `3` turns up, a ball is taken from the first bag, and if any other face turns up a ball is chosen from the second bag. Find the probability of choosing a black ball.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the events
We have two bags:
- **Bag 1**: Contains 3 black balls and 4 white balls (Total = 7 balls)
- **Bag 2**: Contains 4 black balls and 3 white balls (Total = 7 balls)

A die is cast, and based on the outcome, we will choose a ball from one of the bags:
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