Question

twelve of the 20 students in ms. sarnos homeroom are female. each month, ms. sarno randomly selects a student to act as teachers helper. which simulation best models the selection of female teachers helpers for january, february, march, and april? a spinner, divided into 5 congruent sectors with three of the sectors representing female students, is spun 12 times. a coin, with heads up representing female students, is flipped 4 times. a bag of 15 marbles, with 9 marbles representing female students, has a marble drawn 4 times with replacement. a number cube, with odd numbers representing female students, is rolled 12 times.

Explanation:

Step1: Calculate the proportion of female students

The proportion of female students in the homeroom is $\frac{12}{20}=\frac{3}{5}$.

Step2: Analyze each option

Option A

A spinner divided into 5 congruent sectors with 3 sectors representing female students has a probability of $\frac{3}{5}$ for selecting a female - representing sector. But it is spun 12 times instead of 4 times, so it is incorrect.

Option B

A coin has a probability of $\frac{1}{2}$ for heads (representing female students), which is not equal to $\frac{3}{5}$, so it is incorrect.

Option C

In a bag of 15 marbles with 9 marbles representing female students, the probability of drawing a female - representing marble is $\frac{9}{15}=\frac{3}{5}$, and it is drawn 4 times which is the correct number of months, so this option is correct.

Option D

A number cube has 3 odd numbers out of 6, so the probability of getting an odd number (representing female students) is $\frac{3}{6}=\frac{1}{2}$, which is not equal to $\frac{3}{5}$, so it is incorrect.

Answer:

C. A bag of 15 marbles, with 9 marbles representing female students, has a marble drawn 4 times with replacement.