If a coin is flipped and one die is thrown, what is the probability of getting a head or a 4?

Options

A. `1/12`
B. `1/3`
C. `5/12`
D. `7/12`

Explanation

To solve the problem of finding the probability of getting a head or a 4 when a coin is flipped and a die is thrown, we can follow these steps:

### Step 1: Identify the Sample Space
When flipping a coin and rolling a die, we have:
- The outcomes for the coin: Heads (H) or Tails (T).
- The outcomes for the die: 1, 2, 3, 4, 5, or 6.

The total sample space can be represented as pairs (x, y), where x is the outcome of the coin and y is the outcome of the die. Therefore, the sample space is:
- (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)
- (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)

Total outcomes = 2 (from the coin) × 6 (from the die) = 12.

### Step 2: Define the Event
We need to find the probability of the event A, which is getting either a head (H) or a 4 on the die.

### Step 3: Identify Favorable Outcomes
The favorable outcomes for event A can be broken down into two parts:
1. Outcomes where we get a head (H):
- (H, 1)
- (H, 2)
- (H, 3)
- (H, 4)
- (H, 5)
- (H, 6)
(Total = 6 outcomes)

2. Outcomes where we get a 4 on the die:
- (T, 4)
(Total = 1 outcome)

Now we combine these outcomes, but we must be careful not to double count any outcomes. The outcome (H, 4) is already counted in the first part.

So, the total number of favorable outcomes for event A is:
- 6 (from heads) + 1 (from tails with 4) - 1 (for the overlap of (H, 4)) = 6 + 1 - 1 = 6.

### Step 4: Calculate the Probability
The probability of event A is given by the formula:
\[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Thus,
\[ P(A) = \frac{7}{12} \]

### Step 5: Conclusion
The probability of getting a head or a 4 when flipping a coin and rolling a die is \( \frac{7}{12} \).

---