\begin{tabular}{l|l|} What is the \\ probability of \\ rolling a number \\ between 1 and \\ 6 , exclusive? \end{tabular}

To determine the probability of rolling a number **between 1 and 6, exclusive** on a standard six-sided die, let's break it down step by step. ### Understanding the Problem 1. **Standard Die Outcomes**: A standard die has six faces, numbered from **1** to **6**. 2. **Inclusive vs. Exclusive**: - **Inclusive**: Includes the endpoints (1 and 6). - **Exclusive**: Excludes the endpoints (does **not** include 1 and 6). Given the term **"exclusive"**, we're interested in the numbers **greater than 1** and **less than 6**. ### Identifying Favorable Outcomes - **Possible Outcomes on a Die**: {1, 2, 3, 4, 5, 6} - **Favorable Outcomes (Exclusive)**: {2, 3, 4, 5} There are **4 favorable outcomes**. ### Calculating the Probability The probability \( P \) of an event is given by: \[ P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} \] Plugging in the numbers: \[ P(\text{Rolling a number between 1 and 6, exclusive}) = \frac{4}{6} = \frac{2}{3} \approx 0.6667 \text{ or } 66.67\% \] ### Conclusion The probability of rolling a number between **1 and 6, exclusive** on a standard six-sided die is **\(\frac{2}{3}\)**, which is approximately **66.67%**.