If a machine is correctly set up. it produces 90% acceptable items. If it is incorrectly set up, it produces only 40% acceptable items. Past experience shows that 80% of the set ups are correctly done. If after a certain set up, the machine produces 2 acceptable items, find the probability that the machine is correctly setup.

Explanation

To solve the problem, we will use Bayes' theorem, which allows us to find the probability of an event based on prior knowledge of conditions related to the event.

### Step-by-Step Solution:

1. **Define Events**:
- Let \( B_1 \) be the event that the machine is correctly set up.
- Let \( B_2 \) be the event that the machine is incorrectly set up.
- Let \( A \) be the event that the machine produces 2 acceptable items.
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