1. **State the problem:** We have a sample space $S = \{2,3,4,5,6,7,8,9,10,11,12,13\}$. 2. **Define the events:** - Event $E = \{3,4,5,6,7,8\}$ - Event $F = \{7,8,9,10\}$ 3. **List the outcomes in $E$ and $F$:** - Outcomes in $E$ are $3,4,5,6,7,8$ - Outcomes in $F$ are $7,8,9,10$ 4. **Find the intersection $E \cap F$:** $$E \cap F = \{7,8\}$$ 5. **Determine if $E$ and $F$ are mutually exclusive:** - Two events are mutually exclusive if they have no outcomes in common. - Since $E \cap F = \{7,8\} \neq \emptyset$, $E$ and $F$ are **not** mutually exclusive. 6. **Answer:** - Outcomes in $E$ and $F$ are $3,4,5,6,7,8$ and $7,8,9,10$ respectively. - $E$ and $F$ are **not** mutually exclusive because they share outcomes $7$ and $8$. 7. **How to learn more:** - Watch videos on **basic probability concepts**, especially on **sample spaces, events, and mutually exclusive events**. - Look for tutorials explaining **set operations in probability** like union, intersection, and complement. - Practice problems involving listing outcomes and checking mutual exclusivity.