A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B?

Explanation

To solve the problem, we will use Bayes' theorem, which helps us find the probability of an event given prior knowledge of conditions that might be related to the event.

### Step-by-Step Solution:

1. **Define the Events**:
- Let \( A \) be the event that an item is produced by machine A.
- Let \( B \) be the event that an item is produced by machine B.
- Let \( D \) be the event that an item is defective.
...