Question
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Question
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 four times.
A coin is flipped six times and the head appears four times.
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 each time.
Answers
GPT-4o mini
In order for the experimental probability to equal the theoretical probability, the outcomes must reflect the expected probability of the event occurring.
The theoretical probability of getting heads in a fair coin flip is 0.5 (or 50%). When flipping a coin six times, the theoretical probability expects heads to appear about 3 times (which is 50% of 6) on average, but actual results can vary due to randomness.
Among the given options:
1. **A coin is flipped six times and the head appears three times.** - The experimental probability is \( \frac{3}{6} = 0.5 \). This matches the theoretical probability.
2. **A coin is flipped six times and the head appears four times.** - The experimental probability is \( \frac{4}{6} \approx 0.67 \). This does not match the theoretical probability.
3. **A coin is flipped six times and the head appears five times.** - The experimental probability is \( \frac{5}{6} \approx 0.83 \). This does not match the theoretical probability.
4. **A coin is flipped six times and the head appears each time.** - The experimental probability is \( \frac{6}{6} = 1.0 \). This does not match the theoretical probability.
The scenario in which the experimental probability equals the theoretical probability is:
**A coin is flipped six times and the head appears three times.**
The theoretical probability of getting heads in a fair coin flip is 0.5 (or 50%). When flipping a coin six times, the theoretical probability expects heads to appear about 3 times (which is 50% of 6) on average, but actual results can vary due to randomness.
Among the given options:
1. **A coin is flipped six times and the head appears three times.** - The experimental probability is \( \frac{3}{6} = 0.5 \). This matches the theoretical probability.
2. **A coin is flipped six times and the head appears four times.** - The experimental probability is \( \frac{4}{6} \approx 0.67 \). This does not match the theoretical probability.
3. **A coin is flipped six times and the head appears five times.** - The experimental probability is \( \frac{5}{6} \approx 0.83 \). This does not match the theoretical probability.
4. **A coin is flipped six times and the head appears each time.** - The experimental probability is \( \frac{6}{6} = 1.0 \). This does not match the theoretical probability.
The scenario in which the experimental probability equals the theoretical probability is:
**A coin is flipped six times and the head appears three times.**