Describe the Sample Space for the experiment:
A coin is tossed twice and number of heads is recorded.

Answer

To describe the sample space for the experiment of tossing a coin twice and recording the number of heads, we can follow these steps:

### Step 1: Understand the Experiment
We are tossing a coin twice. Each toss can result in either Heads (H) or Tails (T).

### Step 2: List All Possible Outcomes
When a coin is tossed twice, the possible outcomes can be represented as follows:
1. First toss: H, Second toss: H → Outcome: HH
2. First toss: H, Second toss: T → Outcome: HT
3. First toss: T, Second toss: H → Outcome: TH
4. First toss: T, Second toss: T → Outcome: TT

So, the complete set of outcomes when tossing the coin twice is: {HH, HT, TH, TT}.

### Step 3: Count the Number of Heads in Each Outcome
Next, we need to record the number of heads in each of these outcomes:
- HH → 2 heads
- HT → 1 head
- TH → 1 head
- TT → 0 heads

### Step 4: Define the Sample Space
Now, we can summarize the number of heads recorded from the outcomes:
- 0 heads (from TT)
- 1 head (from HT and TH)
- 2 heads (from HH)

Thus, the sample space for the number of heads recorded is:
**Sample Space = {0, 1, 2}**

### Final Answer
The sample space for the experiment of tossing a coin twice and recording the number of heads is {0, 1, 2}.

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