To model the selection of female "teacher's helpers" among the 12 female students from Ms. Sarno's homeroom over the course of four months, we need a simulation that accurately reflects the probability of selecting a female student each time.
The best option from the descriptions provided is:
A bag of 15 marbles, with 9 marbles representing female students, has a marble drawn 4 times with replacement.
Here's why this option is the best:
- Total Students: There are 20 students, with 12 being female, thus the probability of selecting a female student is \( \frac{12}{20} = \frac{3}{5} \).
- Marble Simulation: In this case, using a bag of 15 marbles where 9 represent female students provides a similar ratio. Although it does not exactly match the numbers (since 3 out of 5 is not the same as 9 out of 15), it is sufficient in capturing the concept of selection and replacement.
- With Replacement: Drawing with replacement ensures that each selection remains independent, maintaining the probability of selecting a female for each of the 4 months.
The other options do not appropriately reflect the situation:
- Spinner: Spinning a results in dependent outcomes as it involves separate spins, but it does not adequately model the ratio of female students.
- Coin: A coin flip does not accurately represent the number of female students since there are only two outcomes (heads or tails).
- Number cube: A number cube only produces six outcomes, which does not correlate well with the number of female students.
Thus, using the bag of marbles best simulates the selection of female "teacher's helpers" across those months.