A coin has heads on one side and tails on the other. The coin is tossed 12 times and lands heads up 4 times. Which best describes what happens when the number of trials increases significantly? A. The observed frequency of landing head
The Correct Answer and Explanation is:
Correct Answer: D. The observed frequency of landing heads gets closer to the expected probability of 0.5.
Explanation
When a coin is tossed, there are two possible outcomes: heads or tails. For a fair coin, the probability of each outcome is 0.5, or 50%. This means that, theoretically, if you toss the coin many times, you should get about half heads and half tails.
In the given scenario, the coin is tossed 12 times and lands heads up only 4 times. This gives an observed frequency of heads as: 412=0.333 (or 33.3%)\frac{4}{12} = 0.333\ (\text{or } 33.3\%)
This is less than the expected 50%, but such a result is not unusual in a small sample. With only 12 tosses, random variation can cause noticeable deviations from the theoretical probability.
However, as the number of trials (tosses) increases significantly, the Law of Large Numbers comes into play. This statistical law states that the average of the results obtained from a large number of trials should be close to the expected value—and will tend to get closer as more trials are performed.
So, if you were to toss the coin 1,000 times, or 10,000 times, you’d likely see that the proportion of heads would start to settle around 0.5. The more tosses you perform, the less impact random fluctuations have, and the more the observed frequency (what you actually get) approaches the expected probability (what theory predicts).
In conclusion, while short sequences of coin tosses may show uneven results, over many trials, a fair coin will show close to 50% heads and 50% tails. That’s why the correct choice is D: the observed frequency gets closer to the expected probability of 0.5
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