The experimental probability is equal to the theoretical probability when the number of trials is sufficiently large and the outcomes reflect the expected probabilities accurately. In small sample sizes, like flipping a coin six times, the experimental outcomes can vary significantly from the theoretical expectations.
The theoretical probability of getting heads in a fair coin flip is 0.5.
In the cases presented:
- Head appears five times (5/6 ≈ 0.83)
- Head appears four times (4/6 ≈ 0.67)
- Head appears three times (3/6 = 0.5)
- Head appears each time (6/6 = 1)
Only the third scenario has an experimental probability (0.5) that aligns with the theoretical probability (0.5).
Therefore, the correct response is:
A coin is flipped six times and the head appears three times.