The theoretical probability of flipping a coin and getting heads is \( \frac{1}{2} \). The experimental probability can vary based on the outcomes of the actual flips. In the scenarios you provided, none of the experimental outcomes give a probability that exactly matches the theoretical probability of \( \frac{1}{2} \) in six flips.
- If heads appears 0 times: Experimental probability = 0/6 = 0
- If heads appears 1 time: Experimental probability = 1/6 ≈ 0.167
- If heads appears 2 times: Experimental probability = 2/6 = 0.333
- If heads appears 3 times: Experimental probability = 3/6 = 0.5 (this matches the theoretical probability)
- If heads appears 4 times: Experimental probability = 4/6 ≈ 0.667
- If heads appears 5 times: Experimental probability = 5/6 ≈ 0.833
- If heads appears 6 times: Experimental probability = 6/6 = 1
Therefore, the scenario where the experimental probability equals the theoretical probability is:
A coin is flipped six times and the head appears three times.