Question

Ava surveyed the students in her homeroom about their footwear. She found that 12 students were wearing sneakers, 4 students were wearing boots, and 6 students were wearing dress shoes. She used this data to create a tool that would predict the footwear of randomly chosen students in the school. She placed 2 blue marbles, 3 red marbles, and 6 yellow marbles in a bag, and selected one marble, with replacement, for each student.

What is the predicted footwear of three randomly chosen students if Ava drew two yellow marbles and 1 blue marble?
2 students wearing boots and 1 student wearing sneakers
2 students wearing sneakers and 1 student wearing boots
2 students wearing dress shoes and 1 student wearing boots
2 students wearing sneakers and 1 student wearing dress shoes

Answer 1

To predict the footwear based on the marbles pulled, we first need to identify the corresponding footwear for each color of marble.

From Ava's survey data:
- **Sneakers**: 12 students
- **Boots**: 4 students
- **Dress shoes**: 6 students

Now, let's determine the total number of students surveyed:
Total = 12 (sneakers) + 4 (boots) + 6 (dress shoes) = 22 students.

Next, we find the probability of drawing each color of marble, which corresponds to these footwear types based on the proportions from her survey.

- **Total marbles**: 2 (blue) + 3 (red) + 6 (yellow) = 11 marbles.

Now let's assign the footwear based on the proportion of students wearing each type of footwear:

1. **Sneakers**: \(\frac{12}{22} \approx 0.545\)
2. **Boots**: \(\frac{4}{22} \approx 0.182\)
3. **Dress shoes**: \(\frac{6}{22} \approx 0.273\)

Now, we will assign the colors of marbles based on the probabilities:

1. Since sneakers have the highest proportion, the **yellow marbles** could represent sneakers.
2. Since dress shoes have the next highest proportion, the **red marbles** could represent boots.
3. Since boots have the lowest proportion, the **blue marbles** could represent dress shoes.

Summarizing:
- **Yellow marble**: Sneakers
- **Red marble**: Boots
- **Blue marble**: Dress shoes

According to Ava's experiment, she drew 2 yellow marbles and 1 blue marble. Thus, we assess the predicted footwear:

- **2 Yellow Marbles**: 2 students wearing sneakers.
- **1 Blue Marble**: 1 student wearing dress shoes.

So the predicted footwear for the three randomly chosen students is:

**2 students wearing sneakers and 1 student wearing dress shoes**.

This option corresponds closest to the provided answers as "2 students wearing sneakers and 1 student wearing dress shoes."