Question

jamal performed an experiment flipping a coin. he did 10 trials and then his arm got tired. he recorded his results in the table. 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?

coin	observed frequency	experimental probability
tails	2	0.20

options:

• he should have performed fewer trials before comparing them to the theoretical probability.
• he did not need to perform the experiment to compare theoretical and experimental probabilities.
• he should have subtracted the theoretical probability from the experimental probability.
• he did not perform enough trials to compare the theoretical and experimental probabilities.

Explanation:

For a fair coin, theoretical probability of heads and tails is each \( 0.5 \). Jamal did only 10 trials. With few trials, experimental probability (0.8 for heads, 0.2 for tails) can deviate greatly from theoretical. More trials (like hundreds) are needed for experimental probability to approach theoretical, so his error is insufficient trials for comparison.

Answer:

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