A die is loaded so that the probability of a face `i` is proportional to `i ,i=1,2, 6.` Then find the probability of an even number occurring when the die in rolled.

Explanation

To solve the problem, we need to find the probability of rolling an even number on a loaded die where the probability of each face is proportional to the number on that face.

### Step-by-Step Solution:

1. **Define the Probabilities**:
Since the probability of a face \( i \) (where \( i = 1, 2, 3, 4, 5, 6 \)) is proportional to \( i \), we can express the probabilities as:
- \( P(1) = k \)
- \( P(2) = 2k \)
...