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.

Question

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."