There is a bag with 200 cubes in it. Some of the cubes are red and some are black. You reach into the bag 20 times, each time picking up random cube, recording its color, and putting the cube back in the bag. You picked 7 black cubes and 13 red cubes. With this information, what is the best estimate you can make for how many red cubes and how many black cubes are in the bag?
You pulled black 7 times out of 20.
Let x be estimated number of black cubes in the bag of 200 cubes.
7/20 = x/200
x = ____
Use a similar process for estimating The number of red cubes in the bag.
To determine the best estimate for the number of red and black cubes in the bag, we can use the concept of probability.
Given that you picked 7 black cubes and 13 red cubes out of 20 total picks, we can assume that the ratio of black to red cubes in the bag is approximately equal to the ratio of black to red cubes picked.
To calculate the estimated number of black and red cubes in the bag, we can use the following steps:
1. Calculate the proportions of black and red cubes picked:
- Proportion of black cubes picked: 7/20 = 0.35
- Proportion of red cubes picked: 13/20 = 0.65
2. Multiply the proportions by the total number of cubes in the bag (200) to estimate the quantities:
- Estimated number of black cubes in the bag: 0.35 * 200 = 70
- Estimated number of red cubes in the bag: 0.65 * 200 = 130
Based on this estimation, the best estimate suggests that there are approximately 70 black cubes and 130 red cubes in the bag.
To estimate the number of red and black cubes in the bag, you can use the concept of proportion.
First, calculate the proportion of black cubes in your sample of 20 picks by dividing the number of black cubes picked (7) by the total number of picks (20). This gives you 7/20.
Next, apply this proportion to the total number of cubes in the bag (200). Multiply the proportion of black cubes (7/20) by 200 to estimate the number of black cubes in the bag. This calculation gives you an estimate of 70 black cubes.
To find the number of red cubes, subtract the estimated number of black cubes (70) from the total number of cubes in the bag (200). This will give you an estimate of the number of red cubes, which is 130.
Therefore, the best estimate for the number of red cubes in the bag is 130 and the best estimate for the number of black cubes is 70.