Let's go through Tia's experiment step by step to determine which statement is accurate:
1. Tia flipped a coin 200 times.
2. The coin landed heads up 92 times and tails up 108 times.
We need to evaluate different interpretations of the ratio [tex]\(\frac{92}{200}\)[/tex] based on the given conditions.
### Interpretation of the Ratio [tex]\(\frac{92}{200}\)[/tex]:
1. The ratio [tex]\(\frac{92}{200}\)[/tex] represents the experimental probability of the coin landing heads up in this experiment.
This statement suggests that we are calculating the probability based on the observed outcomes during the experiment. The experimental probability of an event happening (like getting heads) is calculated by dividing the number of times the event occurred by the total number of trials.
In Tia's experiment, the coin landed heads up 92 times out of 200 flips. Therefore, the experimental probability of the coin landing heads up is:
[tex]\[
\frac{\text{Number of heads}}{\text{Total number of flips}} = \frac{92}{200} = 0.46
\][/tex]
This matches the given probability.
2. The ratio [tex]\(\frac{92}{200}\)[/tex] represents the number of trials in this experiment.
The number of trials is the total number of coin flips, which is 200. Therefore, the ratio [tex]\(\frac{92}{200}\)[/tex] does not represent the number of trials (which is simply 200).
3. The ratio [tex]\(\frac{92}{200}\)[/tex] represents the theoretical probability of the coin landing heads up in this experiment.
The theoretical probability of getting heads in a fair coin flip is [tex]\(\frac{1}{2}\)[/tex] or 0.5. This is based on the assumption that the coin is fair, and it does not rely on the actual outcomes of an experiment.
The ratio [tex]\(\frac{92}{200}\)[/tex] is 0.46, which is an observed value from the experiment and not based on theoretical considerations. Therefore, this statement is incorrect for this context.
4. The ratio [tex]\(\frac{92}{200}\)[/tex] represents the number of occurrences of the coin landing heads up in this experiment.
The number of occurrences of heads up is 92. The ratio [tex]\(\frac{92}{200}\)[/tex] contextualizes this number within the total number of trials (200), providing information about probability rather than simply indicating a count. Hence, this statement is incorrect.
### Conclusion:
The correct statement is:
- The ratio [tex]\(\frac{92}{200}\)[/tex] represents the experimental probability of the coin landing heads up in this experiment.
