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

Explanation:

Step1: Match marbles to footwear

We know 12 students wore sneakers, 4 wore boots, and 6 wore dress - shoes. Ava placed 2 blue, 3 red, and 6 yellow marbles. The ratio of students to marbles should be considered for the prediction. Yellow marbles likely represent dress - shoes (since $\frac{6}{2 + 3+6}=\frac{6}{11}$ and $\frac{6}{12 + 4+6}=\frac{6}{22}=\frac{3}{11}$, and the proportion of yellow marbles in the bag is related to the proportion of students wearing dress - shoes). Blue marbles likely represent boots (by similar ratio analysis).

Step2: Interpret the draw

Ava drew 2 yellow marbles and 1 blue marble. Since yellow represents dress - shoes and blue represents boots, the predicted footwear is 2 students wearing dress - shoes and 1 student wearing boots.

Answer:

2 students wearing dress shoes and 1 student wearing boots