There are 3 bags, each containing 5 white balls and 3 black balls. Also there are 2 bags, each containing 2 white balls and 4 black balls. A white ball is drawn at random. Find the probability that this white ball is from a bag of the first group.

Explanation

To find the probability that a white ball drawn at random is from a bag of the first group, we can use Bayes' theorem. Here are the steps to solve the problem:

### Step 1: Define the Events
Let:
- A = event that the white ball is drawn from the first group of bags.
- B = event that a white ball is drawn.

### Step 2: Determine the Total Number of Bags
...