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In which scenario is the experimental probability equal to the theoretical probability?(1 point)

Responses

A coin is flipped six times and the head appears three times.
A coin is flipped six times and the head appears three times.

A coin is flipped six times and the head appears each time.
A coin is flipped six times and the head appears each time.

A coin is flipped six times and the head appears five times.
A coin is flipped six times and the head appears five times.

A coin is flipped six times and the head appears four times.

1 answer

The experimental probability equals the theoretical probability when the outcomes in an experiment reflect the expected probabilities closely.

For a fair coin, the theoretical probability of getting heads is 0.5 (or 50%) in each flip.

Let's analyze the scenarios given:

  1. A coin is flipped six times and the head appears three times.
    Experimental Probability = 3/6 = 0.5
    This matches the theoretical probability of 0.5.

  2. A coin is flipped six times and the head appears each time.
    Experimental Probability = 6/6 = 1.0
    This does not match the theoretical probability of 0.5.

  3. A coin is flipped six times and the head appears five times.
    Experimental Probability = 5/6 ≈ 0.833
    This does not match the theoretical probability of 0.5.

  4. A coin is flipped six times and the head appears four times.
    Experimental Probability = 4/6 ≈ 0.667
    This does not match the theoretical probability of 0.5.

Thus, the scenario where the experimental probability equals the theoretical probability is:

A coin is flipped six times and the head appears three times.