Jamal conducted an experiment by flipping a coin 10 times and recorded the results: 8 heads and 2 tails. Based on these observations, he calculated the experimental probabilities:
- Heads: 8 out of 10 flips, giving an experimental probability of 0.80.
- Tails: 2 out of 10 flips, giving an experimental probability of 0.20.
Jamal then made a prediction that the number of times the coin lands heads up will always be greater than the number of times it lands tails up.
However, this prediction is flawed due to the following reason:
He did not perform enough trials to compare the theoretical and experimental probabilities effectively.
The theoretical probability for a fair coin landing heads or tails is:
- Heads: 0.50
- Tails: 0.50
Given the small number of trials (only 10), the experimental probability can be subject to high variability and may not accurately reflect the true theoretical probabilities. A larger number of trials would be needed to ensure the experimental probabilities converge to the theoretical probabilities based on the Law of Large Numbers.
In conclusion, the error in Jamal's prediction is:
He did not perform enough trials to compare the theoretical and experimental probabilities.
