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

Introduction:
This is one of the simplest probability questions and is a foundational example in elementary probability theory. It involves a single toss of a fair coin and asks for the probability of getting a head. Understanding this example clearly helps build intuition for more complex probability problems.

Given Data / Assumptions:

• The coin is fair, meaning it is not biased.
• The coin has two possible faces: Head (H) and Tail (T).
• The coin is tossed once.
• Each outcome (H or T) is equally likely.
• We must find P(Head).

Concept / Approach:
In a fair coin toss, the sample space (set of possible outcomes) is S = {H, T}. Each outcome has equal probability. For equally likely outcomes, the probability of an event is given by:
P(Event) = (Number of favourable outcomes) / (Total number of outcomes).Here, the event "Head appears" has exactly one favourable outcome: H.

Step-by-Step Solution:
Step 1: Write the sample space.S = {H, T}.Step 2: Count total outcomes.Total number of equally likely outcomes = 2.Step 3: Identify favourable outcomes.Event A = "Getting a head" = {H}.Number of favourable outcomes = 1.Step 4: Compute the probability.P(Head) = 1 / 2.

Verification / Alternative check:
Another way to think about it is symmetry: for a fair coin, there is no reason for head to be more or less likely than tail. The total probability must be 1, and P(H) = P(T). So 2 * P(H) = 1, which again gives P(H) = 1/2.

Why Other Options Are Wrong:
Probability 1 would mean a head is guaranteed every time, which is not true for a fair coin. 1/4 and 0.1 are too small and would be appropriate only in experiments with more outcomes. Probability 0 would mean head can never appear, which contradicts the coin having a head side. Only 1/2 correctly reflects the equal likelihood of head and tail.

Common Pitfalls:
There are usually no major pitfalls in this basic problem, but occasionally learners confuse the probability of "at least one head" in multiple tosses with the single-toss case. Always pay attention to how many times the coin is tossed and exactly what event is being asked about.

Final Answer:
The probability of getting a head in one fair coin toss is 1/2.