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 die is thrown. If it shows up 1 or 3, a ball is taken from the Ist bag but it shows up any other number, a ball is chosen from the II bag. Find the probability of choosing a black ball.

Explanation

To solve the problem, we need to find the probability of choosing a black ball from the two bags based on the outcome of a die throw. Let's break down the solution step by step.

### Step 1: Identify the contents of the bags
- **Bag 1**: 3 black balls and 4 white balls (Total = 7 balls)
- **Bag 2**: 4 black balls and 3 white balls (Total = 7 balls)

### Step 2: Determine the probabilities of choosing each bag based on the die throw
- The die has 6 faces. If it shows 1 or 3, we choose from Bag 1. If it shows 2, 4, 5, or 6, we choose from Bag 2.
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