Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).

Explanation

To find the expected value \( E(X) \) where \( X \) is the larger of two numbers selected at random (without replacement) from the first six positive integers, we will follow these steps:

### Step 1: Identify the Sample Space
When selecting two numbers from the first six positive integers \( \{1, 2, 3, 4, 5, 6\} \), the total number of ways to select two numbers is given by the combination formula \( \binom{n}{r} \), where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose.

\[ \text{Total outcomes} = \binom{6}{2} = 15 \]
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