1. The problem asks for the probability of heads appearing on the 5th toss given that tails appeared on the first four tosses of a fair coin. 2. In a fair coin toss, each toss is independent. This means the outcome of the 5th toss does not depend on the previous tosses. 3. The probability of heads on any single toss of a fair coin is \( \frac{1}{2} \). 4. Therefore, the probability of heads on the 5th toss, regardless of previous outcomes, is \( \frac{1}{2} \). 5. The options given are: - (1) \( \frac{1}{2^4} \) - (2) \( \frac{1}{3} \) - (3) \( \frac{1}{5} \) - (4) \( \frac{1}{4} \) - (5) \( \frac{1}{2} \) 6. The correct answer is option (5): \( \frac{1}{2} \).