Jamal performed an experiment flipping a coin. He did 10 trials and recorded his results in the table below. Based on the experimental probability, Jamal predicted that the number of times the coin lands heads up will always be greater than the number of times it lands tails up. What is the error in his prediction?

\begin{tabular}{|c|c|c|}
\hline
Coin & Observed Frequency & Experimental Probability \\
\hline
Heads & 8 & 0.80 \\
\hline
Tails & 2 & 0.20 \\
\hline
\end{tabular}

A. He should have performed fewer trials before comparing them to the theoretical probability.

B. He did not need to perform the experiment to compare theoretical and experimental probabilities.

C. He should have subtracted the theoretical probability from the experimental probability.

D. He did not perform enough trials to compare the theoretical and experimental probabilities.



Answer :

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.