In a factory which manufactures bolts, machines A. B and C manufacture respectively 25%, 35% and 40% of the bolts. Of their outputs, 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B?

Explanation

To solve the problem, we will use Bayes' theorem to find the probability that a defective bolt was manufactured by machine B.

### Step-by-Step Solution:

1. **Define Events:**
- Let \( M_1 \) be the event that the bolt is manufactured by machine A.
- Let \( M_2 \) be the event that the bolt is manufactured by machine B.
- Let \( M_3 \) be the event that the bolt is manufactured by machine C.
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