Question

In which scenario is the theoretical probability equal to the experimental probability?

A. A coin is flipped 6 times and heads appears 5 times.
B, A coin is flipped 6 times and heads appears 4 times.
C. A coin is flipped 6 times and heads appear 3 times.
D. A coin is flipped 6 times and heads appears all 6 times.

Answer 1

The theoretical probability of getting heads when flipping a fair coin is \( \frac{1}{2} \). To compare this with the experimental probability, we calculate the experimental probability based on the outcomes provided in each scenario.

The experimental probability is given by the formula:

\[
\text{Experimental Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}}
\]

Let's analyze each option:

A. A coin is flipped 6 times and heads appears 5 times.
- Experimental Probability = \( \frac{5}{6} \)

B. A coin is flipped 6 times and heads appears 4 times.
- Experimental Probability = \( \frac{4}{6} = \frac{2}{3} \)

C. A coin is flipped 6 times and heads appears 3 times.
- Experimental Probability = \( \frac{3}{6} = \frac{1}{2} \)

D. A coin is flipped 6 times and heads appears all 6 times.
- Experimental Probability = \( \frac{6}{6} = 1 \)

The only scenario where the experimental probability equals the theoretical probability (which is \( \frac{1}{2} \)) is in option C, where heads appeared 3 times out of 6 flips.

Therefore, the answer is:

**C. A coin is flipped 6 times and heads appears 3 times.**