Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.

Explanation

To solve the problem, we need to find the probability that the transferred ball from Bag I to Bag II is black, given that a red ball is drawn from Bag II after the transfer. We will use Bayes' theorem for this calculation.

### Step-by-Step Solution:

1. **Define Events**:
- Let \( E_1 \): Event that a red ball is transferred from Bag I to Bag II.
- Let \( E_2 \): Event that a black ball is transferred from Bag I to Bag II.
- Let \( A \): Event that a red ball is drawn from Bag II.
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