Question
Ian and Sophia flip a fair coin ten times and record their results; they find that the coin landed on heads eight times.
lan says, “This means the coin will land on heads
more times, our results should be closer to it landing on heads about
Choose the correct answer below.
A. Ian is right, because 8 out of 10 is
B. lan is right, because a coin isn’t neccessarily heads
the population probability.
C. Sophia is right, because of the Law of Large Numbers (Bernoulli’s Theorem).
D. Sophia is right, because the coin should land on heads exactly
lan says, “This means the coin will land on heads
more times, our results should be closer to it landing on heads about
Choose the correct answer below.
A. Ian is right, because 8 out of 10 is
B. lan is right, because a coin isn’t neccessarily heads
the population probability.
C. Sophia is right, because of the Law of Large Numbers (Bernoulli’s Theorem).
D. Sophia is right, because the coin should land on heads exactly
Ask by Parry Moran. in the United States
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Sophia is right because the Law of Large Numbers says that as the number of coin flips increases, the results will get closer to the true probability of 50% for heads.
Solution
C. Sophia is right, because of the Law of Large Numbers (Bernoulli’s Theorem).
Explanation:
Ian and Sophia flipped a fair coin 10 times and observed 8 heads, which is an 80% outcome in this small sample. However, this small number of trials can deviate significantly from the true probability due to random chance.
Sophia’s perspective aligns with the Law of Large Numbers, which states that as the number of trials increases, the sample proportion (in this case, the percentage of heads) will converge to the expected probability (50% for a fair coin). While Ian’s observation is correct for their specific set of 10 flips, Sophia is correct in asserting that with a much larger number of flips, the results should balance out closer to the true probability of 50%.
Why the other options are incorrect:
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A. While Ian correctly states that 8 out of 10 is 80%, he’s incorrectly generalizing this small sample to the true probability of the coin.
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B. This option is confusingly worded and incorrectly attributes Ian’s correctness based on the coin not necessarily being fair, which contradicts the premise that the coin is fair.
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D. Although Sophia is correct that the long-term probability approaches 50%, saying it should land “exactly” 50% of the time is misleading because individual trials can still vary.
Final Answer:
C. Sophia is right, because of the Law of Large Numbers (Bernoulli’s Theorem).
Answered by UpStudy AI and reviewed by a Professional Tutor
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C. Sophia is right, because of the Law of Large Numbers (Bernoulli’s Theorem).
The Law of Large Numbers tells us that as we conduct more trials (in this case, more coin flips), the experimental probability (the actual results of the flips) will get closer to the theoretical probability of the event (which for a fair coin is
This scenario helps illuminate how probabilities work in practice! When flipping a fair coin many times, we expect deviations from the expected
