A single fair coin is tossed once. What is the probability that the outcome is a head?

Introduction / Context:
This is one of the simplest probability questions, designed to test the basic idea of equally likely outcomes. You toss a fair coin once and must find the probability that the result is a head. Even though this feels intuitive, it is important to express it clearly in probability terms.

Given Data / Assumptions:

• The coin is fair, meaning it is not biased.
• There are exactly two possible outcomes: head (H) and tail (T).
• Each outcome is equally likely.
• The coin is tossed once.

Concept / Approach:
When all outcomes are equally likely, probability is defined as: Probability = (Number of favorable outcomes) / (Total number of possible outcomes). Here, favorable outcomes are those in which the coin shows a head. The total possible outcomes are head and tail.

Step-by-Step Solution:
Step 1: List the sample space for one coin toss: {H, T}. Step 2: Total number of possible outcomes = 2. Step 3: The favorable outcome for getting a head is H. Step 4: Number of favorable outcomes = 1. Step 5: Probability of getting a head = 1 / 2.

Verification / Alternative check:
You can imagine performing a large number of coin tosses using a fair coin. Over time, the frequency of heads will get closer and closer to half of the total tosses. This long run frequency interpretation supports the theoretical result that the probability of a head is 1/2. Because the coin is assumed fair, there is no reason to favor one side over the other.

Why Other Options Are Wrong:
Option 1/3 and option 1/4 both imply that there are more possible outcomes than actually exist or that heads is significantly less likely than tails, which contradicts the fairness assumption. Option 2/3 and option 3/4 suggest that heads is more likely than tails, which is not true for a fair coin. None of these alternative fractions correctly represent the symmetric nature of the two outcomes of a coin toss.

Common Pitfalls:
Although this question is simple, it reveals misunderstandings when students mix up the total number of outcomes or misinterpret the term fair. In more complex problems, people sometimes forget that all elementary outcomes must be equally likely before applying the simple favorable over total formula. Establishing this basic idea with a coin toss builds a foundation for approaching more complicated probability questions correctly.

Final Answer:
The probability that the coin shows a head is 1/2.