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 (1, 2, 3, 4, 5, 6), we can follow these steps:

### Step 1: Determine the Sample Space
We need to find all possible pairs of numbers that can be selected from the set {1, 2, 3, 4, 5, 6}. Since we are selecting two numbers without replacement and considering only the larger number, we can list the pairs as follows:

- For 1: (1,2), (1,3), (1,4), (1,5), (1,6)
- For 2: (2,3), (2,4), (2,5), (2,6)
- For 3: (3,4), (3,5), (3,6)
...