Question

A bag contains 150 cubes that are black, yellow and white. A student randomly selects a cube without looking and replaces it in the bag. If the student selected 3 black cubes, 8 yellow cubes and 4 white cubes, which of the options below show a reasonable estimate for the total number of each color cube in the bag? Select all that apply. A) 80 yellow cubes B) 30 black cubes C) 60 black cubes D) 40 white cubes E) 120 yellow cubes

Answer 1

reasonable estimates for the total number of each color cube in the bag are:

B) 30 black cubes (since 750 is too high)

E) 120 yellow cubes (since 280 is too low and 290 is too high)

D) 40 white cubes (since 560 is too low and 570 is too high)

Explanation:

We can use the proportion of each color cube in the student's selection to estimate the total number of each color cube in the bag.

Let's calculate the proportion of each color cube in the selection:

Proportion of black cubes: 3/15 = 0.2

Proportion of yellow cubes: 8/15 = 0.5333...

Proportion of white cubes: 4/15 = 0.2666...

Then, we can use these proportions to estimate the total number of each color cube in the bag by dividing the total number of cubes (150) by each proportion:

Estimated total of black cubes: 150/0.2 = 750

Estimated total of yellow cubes: 150/0.5333 = 281.25 (rounding to 280 or 290)

Estimated total of white cubes: 150/0.2666 = 562.5 (rounding to 560 or 570)