Theoretical probability is based on mathematical calculations and does not involve any physical experiment, whereas experimental probability is based on the results of actual experiments or trials.
In this case, the theoretical probability of getting heads when flipping a fair coin is 0.5 (50%), as there are only two possible outcomes - heads or tails, and they are equally likely.
Now, let's analyze each scenario:
1. A coin is flipped six times and the head appears four times.
This scenario is an experimental probability, which may or may not be equal to the theoretical probability of 0.5.
2. A coin is flipped six times and the head appears five times.
This scenario is an experimental probability, which may or may not be equal to the theoretical probability of 0.5.
3. A coin is flipped six times and the head appears three times.
This scenario is an experimental probability, which may or may not be equal to the theoretical probability of 0.5.
4. A coin is flipped six times and the head appears each time.
This scenario has a theoretical probability of 1 (100%) for getting heads each time, which is not the same as the theoretical probability of 0.5.
Therefore, the scenario where the experimental probability is most likely to equal the theoretical probability is:
A coin is flipped six times and the head appears each time.