What is the number of outcomes when a coin is tossed and then a die is rolled only in case of head is shown on the coin?

Options

A. 6
B. 7
C. 8
D. 5

Answer

To solve the problem of determining the number of outcomes when a coin is tossed and then a die is rolled only if heads is shown on the coin, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Outcomes of Tossing the Coin**:
- When a coin is tossed, there are two possible outcomes: Heads (H) or Tails (T).

2. **Determine the Action Based on Coin Outcome**:
- According to the problem, if the coin shows Heads (H), then a die is rolled. However, if the coin shows Tails (T), the die is not rolled, and we do not consider any outcomes from the die.

3. **List the Outcomes for Each Case**:
- If the coin shows Heads (H), the die can show any of the following outcomes: 1, 2, 3, 4, 5, or 6. Thus, the outcomes when the coin shows Heads are:
- H1 (H and die shows 1)
- H2 (H and die shows 2)
- H3 (H and die shows 3)
- H4 (H and die shows 4)
- H5 (H and die shows 5)
- H6 (H and die shows 6)
- If the coin shows Tails (T), there are no die outcomes, so we only have T.

4. **Combine the Outcomes**:
- The complete set of outcomes can be represented as:
- H1, H2, H3, H4, H5, H6, T
- This gives us a total of 7 outcomes.

5. **Count the Total Number of Outcomes**:
- The total number of outcomes is 7.

### Final Answer:
The total number of outcomes when a coin is tossed and a die is rolled only if heads is shown on the coin is **7**.

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