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 two bags based on the outcome of a die roll. Here’s a step-by-step solution:

### Step 1: Define the Events
Let:
- \( E_1 \): Event of choosing from Bag 1 (when the die shows 1 or 3)
- \( E_2 \): Event of choosing from Bag 2 (when the die shows 2, 4, 5, or 6)
- \( E_3 \): Event of choosing a black ball

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