Which of the following correctly represents the sample space $S$ for a single toss of a fair coin?

• A. $\left\{T\right\}$
• B. $\left\{H\right\}$
• C. $\{H,T,\mathrm{HH}\}$
• D. $\{H,T\}$

Answer: (D)

Verified step by step guidance

1. Understand that the sample space \( S \) of an experiment is the set of all possible outcomes that can occur when the experiment is performed.
2. For a single toss of a fair coin, identify all possible outcomes. Since the coin can land either on Heads (H) or Tails (T), these are the only two outcomes.
3. Write the sample space as a set containing these outcomes: \( S = \{ H, T \} \). This means the sample space includes both Heads and Tails, but no other outcomes.
4. Check the given options and compare them to the correct sample space. The set \( \{ H \} \) or \( \{ T \} \) alone are incomplete because they do not include both possible outcomes.
5. Also, the set \( \{ H, T, HH \} \) is incorrect because \( HH \) is not a possible outcome for a single toss; it might represent two tosses, which is outside the scope of this problem.