Question
In which scenario is the theoretical probability equal to the experimental probability?(1 point)
Responses
A coin is flipped 6 times and heads appears 5 times.
A coin is flipped 6 times and heads appears 5 times.
A coin is flipped 6 times and heads appears 4 times.
A coin is flipped 6 times and heads appears 4 times.
A coin is flipped 6 times and heads appear 3 times.
A coin is flipped 6 times and heads appear 3 times.
A coin is flipped 6 times and heads appears all 6 times.
A coin is flipped 6 times and heads appears all 6 times.
Responses
A coin is flipped 6 times and heads appears 5 times.
A coin is flipped 6 times and heads appears 5 times.
A coin is flipped 6 times and heads appears 4 times.
A coin is flipped 6 times and heads appears 4 times.
A coin is flipped 6 times and heads appear 3 times.
A coin is flipped 6 times and heads appear 3 times.
A coin is flipped 6 times and heads appears all 6 times.
A coin is flipped 6 times and heads appears all 6 times.
Answers
GPT-4o mini
The theoretical probability of getting heads when flipping a fair coin is 0.5 (or 50%). The experimental probability is calculated based on the actual outcomes of the flips.
Let's analyze the scenarios:
1. **A coin is flipped 6 times and heads appears 5 times.**
- Experimental probability = 5/6 ≈ 0.833, theoretical is 0.5.
2. **A coin is flipped 6 times and heads appears 4 times.**
- Experimental probability = 4/6 ≈ 0.667, theoretical is 0.5.
3. **A coin is flipped 6 times and heads appears 3 times.**
- Experimental probability = 3/6 = 0.5, theoretical is also 0.5.
4. **A coin is flipped 6 times and heads appears all 6 times.**
- Experimental probability = 6/6 = 1, theoretical is 0.5.
Out of these, the **third scenario** (3 heads out of 6 flips) has both the experimental probability and the theoretical probability equal to 0.5.
Therefore, the answer is: **A coin is flipped 6 times and heads appears 3 times.**
Let's analyze the scenarios:
1. **A coin is flipped 6 times and heads appears 5 times.**
- Experimental probability = 5/6 ≈ 0.833, theoretical is 0.5.
2. **A coin is flipped 6 times and heads appears 4 times.**
- Experimental probability = 4/6 ≈ 0.667, theoretical is 0.5.
3. **A coin is flipped 6 times and heads appears 3 times.**
- Experimental probability = 3/6 = 0.5, theoretical is also 0.5.
4. **A coin is flipped 6 times and heads appears all 6 times.**
- Experimental probability = 6/6 = 1, theoretical is 0.5.
Out of these, the **third scenario** (3 heads out of 6 flips) has both the experimental probability and the theoretical probability equal to 0.5.
Therefore, the answer is: **A coin is flipped 6 times and heads appears 3 times.**