The scenario in which the experimental probability is equal to the theoretical probability is typically one where the number of trials is very high, allowing for the experimental results to converge to the theoretical results. However, given the options provided, none of the experimental probabilities calculated from these scenarios will equal the theoretical probability of getting heads when flipping a fair coin.
The theoretical probability of getting heads on a single flip of a fair coin is \(0.5\).
Let's analyze the options:
-
A coin is flipped six times and the head appears five times.
Experimental Probability of heads = \( \frac{5}{6} \) (approximately 0.83) -
A coin is flipped six times and the head appears four times.
Experimental Probability of heads = \( \frac{4}{6} \) (approximately 0.67) -
A coin is flipped six times and the head appears three times.
Experimental Probability of heads = \( \frac{3}{6} \) (0.50) -
A coin is flipped six times and the head appears each time.
Experimental Probability of heads = \( \frac{6}{6} \) (1.00)
The only scenario where the experimental probability matches the theoretical probability of 0.5 is the third one:
A coin is flipped six times and the head appears three times.