The experimental probability being equal to the theoretical probability typically occurs when the number of trials is sufficiently large, and the outcomes are randomly distributed according to the theoretical expectations.
In the case of flipping a fair coin, the theoretical probability of getting heads (H) is 0.5 (or 50%) for each flip. However, experimental probability varies based on actual results.
Here's a breakdown of the scenarios given:
-
A coin is flipped six times and the head appears each time.
- Experimental probability of heads = 6/6 = 1 (or 100%)
- Theoretical probability = 0.5
- Not equal.
-
A coin is flipped six times and the head appears four times.
- Experimental probability of heads = 4/6 = 2/3 (or approximately 66.67%)
- Theoretical probability = 0.5
- Not equal.
-
A coin is flipped six times and the head appears three times.
- Experimental probability of heads = 3/6 = 0.5 (or 50%)
- Theoretical probability = 0.5
- Equal!
-
A coin is flipped six times and the head appears five times.
- Experimental probability of heads = 5/6 (or approximately 83.33%)
- Theoretical probability = 0.5
- Not equal.
Thus, the scenario in which the experimental probability is equal to the theoretical probability is when a coin is flipped six times and the head appears three times.