The experimental probability approximates the theoretical probability as the number of trials increases. However, in the scenarios provided, the theoretical probability of getting heads when flipping a fair coin is 0.5 (or 50%).
In this case, if a coin is flipped six times, the theoretical probability of getting heads 3 times is a situation that aligns with the theoretical expectations of a fair coin, as it would mean landing heads roughly half the time in a small sample.
The scenario where the experimental probability could equal the theoretical probability (0.5) is:
- A coin is flipped six times and the head appears three times.
In this scenario, the experimental probability of getting heads is \( \frac{3}{6} = 0.5 \), which matches the theoretical probability of 0.5 for a fair coin.