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.
.

Question

UpStudy AI · Accepted Answer

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.
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:** A small number of tosses isn't enough to determine if a coin is unfair. More tosses are needed to see if the results are balanced.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Probability Questions