To solve this problem, we need to determine the correct graph that models the expected probability of each outcome in the sample space \( S = {1, 2, 3, 4, 5} \).
Since each outcome is equally likely, the probability of each outcome is given by the formula:
\[ P(X = x) = \frac{1}{n} \]
where \( n \) is the total number of outcomes. Here, \( n = 5 \) (the numbers 1 through 5). Thus, the probability of each outcome is:
\[ P(X = x) = \frac{1}{5} = 0.2 \]
Therefore, the expected probability for each of the outcomes (1, 2, 3, 4, 5) is 0.2.
Now let's analyze the graphs:
- Graph 1: Shows probabilities from 0 to 6 - this range is incorrect since the probabilities exceed 1.
- Graph 2: The y-axis shows probabilities from 0 to 0.25 in increments of 0.05. This is a suitable range and appears to have values of 0.2 (which corresponds to each outcome).
- Graph 3: Shows probabilities from 0 to 2.5, which again exceed 1.
Based on this analysis, Graph 2 is the correct one that models the expected probabilities for the outcomes {1, 2, 3, 4, 5}. Each outcome shown will have a height of 0.2, representing the expected probability of each outcome occurring.