A coin is tossed and a single 6-sided die is rolled. Find the probability of getting the head side of the coin and getting a 3 on the die.

Answer

To solve the problem of finding the probability of getting heads when tossing a coin and rolling a 3 on a 6-sided die, we can follow these steps:

### Step-by-step Solution:

1. **Identify the Events**:
- Event A: Getting heads on the coin toss.
- Event B: Getting a 3 on the die roll.

2. **Determine the Total Outcomes for Each Event**:
- For the coin toss, there are 2 possible outcomes: Heads (H) or Tails (T).
- For the 6-sided die, there are 6 possible outcomes: 1, 2, 3, 4, 5, 6.

3. **Calculate the Total Outcomes for Both Events**:
- Since the coin toss and the die roll are independent events, the total number of combined outcomes is the product of the individual outcomes:
\[ \text{Total Outcomes} = \text{Outcomes for Coin} \times \text{Outcomes for Die} = 2 \times 6 = 12 \]

4. **Identify the Favorable Outcomes**:
- We need to find the favorable outcomes for getting heads and rolling a 3. The only combination that satisfies both conditions is (H, 3).
- Therefore, there is only **1 favorable outcome**: Heads and 3.

5. **Calculate the Probability**:
- The probability of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
- Substituting the values we found:
\[ P(\text{Heads and 3}) = \frac{1}{12} \]

### Final Answer:
The probability of getting heads on the coin and rolling a 3 on the die is \(\frac{1}{12}\).