8. An unbiased coin is tossed 100 times in experiment I and 1000 times in experiment II. Which one of the
following statements is most likely to be TRUE regarding the ratio between heads and tails in experiment I
and II?
1. It will be closer to one in experiment I
2. It will be closer to one in experiment II
3. It will be equal to one in both experiments
4. It will be equally away from one in both experiments
Understanding the Law of Large Numbers in Coin Toss Experiments
When tossing an unbiased coin, we expect an equal number of heads and tails over a large number of trials. But in practice, short experiments can show fluctuations due to random chance. Let’s analyze a specific case where this principle comes into play.
The Problem:
Two experiments are conducted:
-
Experiment I: A fair coin is tossed 100 times
-
Experiment II: A fair coin is tossed 1000 times
The question is:
Which of the following statements is most likely to be TRUE regarding the ratio between heads and tails?
Options:
-
It will be closer to one in experiment I
-
It will be closer to one in experiment II
-
It will be equal to one in both experiments
-
It will be equally away from one in both experiments
Explanation:
The law of large numbers is a fundamental statistical principle that states:
As the number of trials in a random experiment
