Question

what event has exactly 12 possible outcoms
tossing a coin and randomly choosing one of 4 different cards
tossing a coin 6 times
rolling a number cube with sides labeled 1 through 6 and tossing a coin
rolling a number cute with sides labeled 1 through 6 and then rolling the number cube again

Answer 1

To determine which event has exactly 12 possible outcomes, we can analyze each option:

1. **Tossing a coin and randomly choosing one of 4 different cards**:
- Tossing a coin has 2 possible outcomes (Heads or Tails).
- Choosing one of 4 cards has 4 possible outcomes.
- Thus, the total number of outcomes is \(2 \times 4 = 8\).

2. **Tossing a coin 6 times**:
- Each coin toss has 2 outcomes.
- For 6 tosses, the total number of outcomes is \(2^6 = 64\).

3. **Rolling a number cube with sides labeled 1 through 6 and tossing a coin**:
- Rolling the number cube has 6 possible outcomes (1 through 6).
- Tossing a coin has 2 possible outcomes.
- The total number of outcomes is \(6 \times 2 = 12\).

4. **Rolling a number cube with sides labeled 1 through 6 and then rolling the number cube again**:
- The first roll has 6 outcomes, and the second roll also has 6 outcomes.
- The total number of outcomes is \(6 \times 6 = 36\).

Therefore, the event that has exactly 12 possible outcomes is **rolling a number cube with sides labeled 1 through 6 and tossing a coin**.