1. **Problem:** Identify 5 examples of non-mutually exclusive events with explanations. 2. **Definition:** Non-mutually exclusive events are events that can occur at the same time, meaning their intersection is not empty. Formally, events $A$ and $B$ are non-mutually exclusive if $P(A \cap B) > 0$. 3. **Example 1:** Drawing a card from a deck. Let $A$ = drawing a red card, $B$ = drawing a face card. These events are non-mutually exclusive because some cards (like the red face cards: Jack, Queen, King of hearts and diamonds) belong to both $A$ and $B$. 4. **Example 2:** Rolling a die. Let $A$ = rolling an even number, $B$ = rolling a number greater than 3. The events overlap on numbers 4 and 6, so $P(A \cap B) > 0$. 5. **Example 3:** Selecting a student. Let $A$ = student is female, $B$ = student is in the math club. Some female students can be in the math club, so these events are non-mutually exclusive. 6. **Example 4:** Tossing two coins. Let $A$ = first coin is heads, $B$ = second coin is heads. Both coins can be heads simultaneously, so $P(A \cap B) > 0$. 7. **Example 5:** Weather events. Let $A$ = it rains today, $B$ = it is windy today. It can be both rainy and windy, so these events are non-mutually exclusive. 8. **Summary:** In all these examples, the events can happen together, so they are non-mutually exclusive with $P(A \cap B) > 0$.