A coin is tossed and then a die is rolled only in case a head is shown on the coin.

Explanation

To solve the problem step by step, we will first identify the sample space and then analyze the events based on the outcomes of the coin toss and the die roll.

### Step 1: Identify the outcomes of the coin toss
When a coin is tossed, there are two possible outcomes:
- Head (H)
- Tail (T)

### Step 2: Determine the action based on the coin toss
According to the problem, if the coin shows a head (H), we will roll a die. If the coin shows a tail (T), we do not roll the die.

### Step 3: Identify the outcomes when the die is rolled
If the coin shows a head (H), the outcomes from rolling a die are:
- 1
- 2
- 3
- 4
- 5
- 6

### Step 4: Construct the sample space
Now we can construct the complete sample space (S) for the experiment:
- If the coin shows a head (H), the outcomes are: H1, H2, H3, H4, H5, H6 (where H represents the head and the number represents the die outcome).
- If the coin shows a tail (T), the outcome is: T (since we do not roll the die).

Thus, the complete sample space (S) is:
S = {H1, H2, H3, H4, H5, H6, T}

### Step 5: Count the total number of outcomes
Now, we count the total number of outcomes in the sample space:
- There are 6 outcomes when the coin shows a head (H) and 1 outcome when it shows a tail (T).
- Therefore, the total number of outcomes = 6 (from H) + 1 (from T) = 7.

### Final Result
The total number of outcomes in the sample space is 7.

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