Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag II.

Explanation

To solve the problem, we will use Bayes' theorem to find the probability that the red ball was drawn from Bag II given that a red ball was drawn.

### Step-by-Step Solution:

1. **Define Events:**
- Let \( R \) be the event that a red ball is drawn.
- Let \( B_1 \) be the event that the ball is drawn from Bag I.
- Let \( B_2 \) be the event that the ball is drawn from Bag II.
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