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 understand Ava's prediction based on her marble drawing system:

1. Marble Colors and Footwear Correspondence:
   • 2 blue marbles correspond to boots (4 boots out of 22 total shoes means about \( \frac{4}{22} \) chance of boots = ~18%).
   • 3 red marbles correspond to sneakers (12 sneakers out of 22 total shoes means about \( \frac{12}{22} \) chance of sneakers = ~55%).
   • 6 yellow marbles correspond to dress shoes (6 dress shoes out of 22 total shoes means about \( \frac{6}{22} \) chance of dress shoes = ~27%).

Now, according to the selection:

• Ava drew 2 yellow marbles, which represent dress shoes.
• Ava drew 1 blue marble, which represents boots.

Putting this together:

• The predicted footwear for the three students based on the drawn marbles would be:
  • 2 students wearing dress shoes (from 2 yellow marbles)
  • 1 student wearing boots (from 1 blue marble)

So, based on her selections, the correct prediction is two students wearing dress shoes and one student wearing boots. However, that specific choice is not among the given options. The closest match from the list would be:

2 students wearing boots and 1 student wearing sneakers would be the same logic applied but not matching the draw specifically.

Thus it's concluded that the selection gives 2 dress shoes and 1 boot but the options don't include this exact configuration.