Let's analyze the given statements one by one to determine which is true.
First, we need to understand a few key terms:
1. Experimental Probability: This is calculated based on the outcomes of an actual experiment. It is given by the ratio of the number of successful occurrences to the total number of trials.
2. Theoretical Probability: This is based on the expected outcomes given a perfect model. For a fair coin, the theoretical probability of landing heads up is [tex]\(\frac{1}{2}\)[/tex] since both outcomes (heads and tails) are equally likely.
Given the information:
- Tia flipped the coin 200 times (the total number of trials).
- The coin landed heads up 92 times.
- Hence, the coin landed tails up [tex]\( 200 - 92 = 108 \)[/tex] times.
Now, let's evaluate each statement:
1. "The ratio [tex]\(\frac{92}{200}\)[/tex] represents the experimental probability of the coin landing heads up in this experiment."
- The experimental probability is calculated as [tex]\(\frac{\text{number of heads}}{\text{total flips}}\)[/tex].
- Here, it would be [tex]\(\frac{92}{200}\)[/tex].
- This statement correctly describes the experimental probability based on the experiment's outcomes.
2. "The ratio [tex]\(\frac{92}{200}\)[/tex] represents the number of trials in this experiment."
- The number of trials is simply 200, which is the total number of times the coin is flipped.
- The ratio [tex]\(\frac{92}{200}\)[/tex] does not directly reflect the number of trials but rather the fraction of heads in the total flips.
3. "The ratio [tex]\(\frac{92}{200}\)[/tex] represents the theoretical probability of the coin landing heads up in this experiment."
- The theoretical probability for a fair coin landing heads up is always [tex]\(\frac{1}{2}\)[/tex], not [tex]\(\frac{92}{200}\)[/tex].
- This statement is incorrect because it confuses experimental probability with theoretical probability.
4. "The ratio [tex]\(\frac{92}{200}\)[/tex] represents the number of occurrences of the coin landing heads up in this experiment."
- The ratio [tex]\(\frac{92}{200}\)[/tex] isn't a direct count but a fraction representing how often heads occurred relative to the total trials.
- The number of occurrences is 92, not the ratio.
Comparing all four statements, the true statement is:
"The ratio [tex]\(\frac{92}{200}\)[/tex] represents the experimental probability of the coin landing heads up in this experiment."
