Which of the following pairs of events are mutually exclusive ($AB=\; 15$)?

• A. Selecting a student: Event $A$ is being left-handed, Event $B$ is being a sophomore
• B. Rolling a die: Event $A$ is getting an even number, Event $B$ is getting an odd number
• C. Drawing a card: Event $A$ is drawing a heart, Event $B$ is drawing a queen
• D. Flipping a coin: Event $A$ is getting heads, Event $B$ is getting tails

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the definition of mutually exclusive events. Two events are mutually exclusive if they cannot happen at the same time. In other words, the intersection of the two events is empty: \(A \cap B = \emptyset\).
2. Step 2: Analyze each pair of events to see if they can occur simultaneously. For example, consider the pair 'being left-handed' and 'being a sophomore'. A student can be both left-handed and a sophomore, so these events are not mutually exclusive.
3. Step 3: For the pair 'getting an even number' and 'getting an odd number' when rolling a die, note that a single roll cannot result in both an even and an odd number simultaneously. Therefore, these events are mutually exclusive.
4. Step 4: For the pair 'drawing a heart' and 'drawing a queen' from a deck of cards, consider that the queen of hearts exists, so these events can occur together. Hence, they are not mutually exclusive.
5. Step 5: For the pair 'getting heads' and 'getting tails' when flipping a coin, a single flip cannot be both heads and tails at the same time, so these events are mutually exclusive.