A die is thrown three times. Let `X` be the number of twos seen. Find the expectation of `X` .

Explanation

To find the expectation of \( X \), where \( X \) is the number of twos seen when a die is thrown three times, we can follow these steps:

### Step 1: Define the Random Variable
Let \( X \) be the number of times a two appears when a die is thrown three times. The possible values of \( X \) are \( 0, 1, 2, \) and \( 3 \).

### Step 2: Calculate the Probability of Each Value of \( X \)

1. **Probability that \( X = 0 \)**:
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