A student tosses a coin 3 times, and a head appears each time. The student concludes that the coin is not fair. What is your response? Which of the following is a correct response to the statement? A. Tossing three heads on the first three tosses of a coin does imply the coin is unfair. Only when a fair coin is tossed a few times can we expect to get approximately equal numbers of tails and heads. B. Tossing three heads on the first three tosses of a coin does imply the coin is unfair. C. Tossing three heads on the first three tosses of a coin does not imply the coin is unfair. Only when a fair coin is tossed a few times can we expect to get approximately equal numbers of tails and heads. D. Tossing three heads on the first three tosses of a coin does not imply the coin is unfair. Only when a fair coin is tossed a much greater number of times can we expect to get approximately equal numbers of tails and heads. .

The correct response is: **D. Tossing three heads on the first three tosses of a coin does not imply the coin is unfair. Only when a fair coin is tossed a much greater number of times can we expect to get approximately equal numbers of tails and heads.** **Explanation:** When evaluating whether a coin is fair, observing the outcomes of a small number of tosses (like three) is not sufficient evidence to draw a definitive conclusion. Here's why: - **Probability of Three Heads in a Row:** For a fair coin, the probability of getting heads on a single toss is 0.5. Therefore, the probability of getting three heads in a row is \( (0.5)^3 = 0.125 \) or 12.5%. While this outcome is somewhat unlikely, it is still within the realm of possibility for a fair coin. - **Sample Size Matters:** Small sample sizes can exhibit greater variability, meaning that unusual sequences can occur by chance. To make a more reliable assessment of the coin's fairness, a larger number of tosses would be necessary. With a larger sample size, the results are more likely to reflect the true probability of heads and tails, providing a clearer indication of whether the coin is biased. - **Statistical Significance:** In statistics, conclusions about fairness or bias typically require sufficient evidence. A few tosses do not provide enough data to achieve statistical significance. Only with a larger number of trials can we confidently determine if there's a consistent bias toward heads or tails. In summary, while getting three heads in a row might raise a suspicion, it is not enough evidence on its own to conclude that a coin is unfair. More extensive testing is needed to make an informed judgment.