Let's go through the explanation step-by-step to determine which statement about Tia's experiment is true.
In this experiment, Tia flipped a coin 200 times, and the coin landed heads up 92 times. The different statements provided need to be evaluated based on these numbers.
1. The ratio [tex]\(\frac{92}{200}\)[/tex] represents the experimental probability of the coin landing heads up in this experiment.
To understand this, let's recall the definition of experimental probability. Experimental probability is the ratio of the number of times an event occurs to the total number of trials. In this case, the event is the coin landing heads up.
The number of times the coin landed heads up = 92\
The total number of trials (flips) = 200
Thus, the experimental probability of the coin landing heads up is calculated as follows:
[tex]\[
\text{Experimental probability} = \frac{\text{Number of heads}}{\text{Total number of trials}} = \frac{92}{200} = 0.46
\][/tex]
Therefore, this statement is accurate.
2. The ratio [tex]\(\frac{92}{200}\)[/tex] represents the number of trials in this experiment.
The number of trials in Tia's experiment is 200, and not a ratio. Hence, this statement is incorrect.
3. The ratio [tex]\(\frac{92}{200}\)[/tex] represents the theoretical probability of the coin landing heads up in this experiment.
Theoretical probability is calculated based on the expected outcomes under ideal conditions. For a fair coin, the theoretical probability of landing heads up is [tex]\(\frac{1}{2} \text{ or } 0.5\)[/tex]. However, the ratio [tex]\(\frac{92}{200} \text{ or } 0.46\)[/tex] is based on actual outcomes from Tia's experiment, not the theoretical expectation. So, this statement is incorrect.
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] is a fraction, not a whole number. The number of occurrences of heads is 92, which is just the numerator of the ratio. Thus, this statement is incorrect.
Given the analysis of each statement, the correct one is:
The ratio [tex]\(\frac{92}{200}\)[/tex] represents the experimental probability of the coin landing heads up in this experiment.
