If a fair coin is tossed twice, what is the probability of obtaining at least one head?

1. Analyze the question

We are tossing a fair coin twice. We need to find the probability of getting at least one head. "At least one" means we are looking for the outcomes that have either one head or two heads.

2. Explain the concept

When tossing a coin, there are two possible outcomes for each toss: Head (H) or Tail (T). When tossing a coin twice, the total number of possible outcomes is calculated as $2^n$, where $n$ is the number of tosses. Here, $2^2 = 4$.

The sample space (all possible outcomes) is:

• (H, H) — Two heads
• (H, T) — Head then Tail
• (T, H) — Tail then Head
• (T, T) — Two tails

3. Show the solution

• Total outcomes: 4
• Favorable outcomes (at least one head): • (H, H) - Yes • (H, T) - Yes • (T, H) - Yes • (T, T) - No (This has zero heads)

There are 3 favorable outcomes.

Probability formula:

Converting the fraction to a decimal:

4. Identify the answer

Comparing our result to the options provided, the correct choice is B.

5. Exam Tip

Whenever you see the phrase "at least one," it is often easier to use the complement rule:

The only outcome with "no heads" is (T, T), which has a probability of $\frac{1}{4}$ (or 0.25). So, $1 - 0.25 = 0.75$. This trick saves time in exams!