2. Suppose you draw one card from a deck of 52 cards. Consider the event of drawing a number less than 5 or a red card. Are these events mutually exclusive?

To determine if the events of drawing a number less than 5 or a red card are mutually exclusive, we need to analyze the two events: 1. **Event A: Drawing a number less than 5** - The numbers less than 5 in a standard deck of cards are 2, 3, and 4. - There are 4 suits (hearts, diamonds, clubs, spades), so: - 2 of hearts - 2 of diamonds - 3 of hearts - 3 of diamonds - 4 of hearts - 4 of diamonds - This gives us a total of 6 cards that are less than 5. 2. **Event B: Drawing a red card** - The red cards in a standard deck are the hearts and diamonds. - There are 26 red cards in total (13 hearts + 13 diamonds). Next, we need to check if these two events can occur at the same time (i.e., if they have any common outcomes): - The cards that are less than 5 (2, 3, 4) that are also red are: - 2 of hearts - 2 of diamonds - 3 of hearts - 3 of diamonds - 4 of hearts - 4 of diamonds From this, we can see that there are red cards (2, 3, and 4 of hearts and diamonds) that are also less than 5. Therefore, these two events are not mutually exclusive because they can occur simultaneously. ### Conclusion: The events of drawing a number less than 5 and drawing a red card are **not mutually exclusive**.