Three bags contain balls as shown in the table below: Bag Number of White balls Number of Black balls Number of Red balls I 1 2 3 II 2 1 1 III 4 3 2 A bag is chosen at random and two balls are drawn from it. They happen to be white and red. What is the probability that they came from the III bag?

Explanation

To solve the problem, we will use Bayes' theorem to find the probability that the two drawn balls (one white and one red) came from Bag III.

### Step-by-Step Solution:

**Step 1: Define the events**
- Let \( B_1 \), \( B_2 \), and \( B_3 \) be the events of choosing Bag I, Bag II, and Bag III respectively.
- Let \( E \) be the event of drawing one white ball and one red ball.

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