Answer :
To determine the type of probability that best describes the scenario involving Rhea's experiment with drawing marbles, let's carefully analyze the situation.
Step 1: Understanding the Scenario
Rhea conducted an experiment where she randomly drew a marble from a bag, noted its color, and then put it back into the bag. She repeated this process 21 times. Out of these 21 trials, she drew a yellow marble 7 times.
Step 2: Calculating the Probability
Rhea observed that out of the 21 trials, drawing a yellow marble occurred 7 times. She concluded that the probability of drawing a yellow marble is given by:
[tex]\[ P(\text{Yellow}) = \frac{\text{Number of times yellow was drawn}}{\text{Total number of trials}} = \frac{7}{21} = \frac{1}{3} \][/tex]
Step 3: Identifying the Type of Probability
To classify the type of probability Rhea used, let's consider the definitions of different types of probabilities:
- Random Probability: This is not a standard term in probability theory and can generally mean any kind of probabilistic event involving chance.
- Unpredictable Probability: This is also not a standard term in probability theory. Probability itself deals with predicting the likelihood of events, not the certainty.
- Theoretical Probability: This type of probability is based on known possible outcomes and their equally likely chances. It is often derived from reasoning about the structure of the problem (for example, in a fair die, the probability of any specific outcome is theoretically [tex]\( \frac{1}{6} \)[/tex]).
- Empirical Probability: This type of probability, also known as experimental probability, is calculated based on actual observations or experiments. It involves conducting trials and using the outcomes to estimate the likelihood of events.
In Rhea's experiment, she determined the probability based on her actual observations from repeated trials. She did not use assumptions about the theoretical setup of the problem but rather relied on her empirical data. This aligns with the definition of empirical probability.
Conclusion
Given the provided options and the analysis above, the type of probability Rhea used in her experiment is best described by:
D. Empirical
Thus, the answer is:
[tex]\[ \boxed{4} \][/tex]
Step 1: Understanding the Scenario
Rhea conducted an experiment where she randomly drew a marble from a bag, noted its color, and then put it back into the bag. She repeated this process 21 times. Out of these 21 trials, she drew a yellow marble 7 times.
Step 2: Calculating the Probability
Rhea observed that out of the 21 trials, drawing a yellow marble occurred 7 times. She concluded that the probability of drawing a yellow marble is given by:
[tex]\[ P(\text{Yellow}) = \frac{\text{Number of times yellow was drawn}}{\text{Total number of trials}} = \frac{7}{21} = \frac{1}{3} \][/tex]
Step 3: Identifying the Type of Probability
To classify the type of probability Rhea used, let's consider the definitions of different types of probabilities:
- Random Probability: This is not a standard term in probability theory and can generally mean any kind of probabilistic event involving chance.
- Unpredictable Probability: This is also not a standard term in probability theory. Probability itself deals with predicting the likelihood of events, not the certainty.
- Theoretical Probability: This type of probability is based on known possible outcomes and their equally likely chances. It is often derived from reasoning about the structure of the problem (for example, in a fair die, the probability of any specific outcome is theoretically [tex]\( \frac{1}{6} \)[/tex]).
- Empirical Probability: This type of probability, also known as experimental probability, is calculated based on actual observations or experiments. It involves conducting trials and using the outcomes to estimate the likelihood of events.
In Rhea's experiment, she determined the probability based on her actual observations from repeated trials. She did not use assumptions about the theoretical setup of the problem but rather relied on her empirical data. This aligns with the definition of empirical probability.
Conclusion
Given the provided options and the analysis above, the type of probability Rhea used in her experiment is best described by:
D. Empirical
Thus, the answer is:
[tex]\[ \boxed{4} \][/tex]
