Question

A tub has 50 small balls. Some balls are white, and summer orange. Without being able to see into the tub, each student in a class of 25 is allowed to pick a ball out of the tub at random. The color of the ball is recorded, and the ball is put back into the tub. At the end, seven orange balls and 18 white balls were picked. What is the best estimate you can give for the number of orange balls in the number of white balls in the tub? Describe how to calculate this best estimate, and explain why your method of calculation makes sense in a way that a seventh grader my understand. Is your best estimate necessarily accurate? Why or why not?

Answer 1

The best estimate we can give for the number of orange balls in the tub is 7, and the number of white balls in the tub is 43.

To calculate this, we take the number of orange balls picked (7) and divide it by the total number of balls picked (25) to get the proportion of orange balls in the tub. Then we multiply that proportion by the total number of balls in the tub (50) to get our estimate for the number of orange balls in the tub.

7 / 25 = 0.28

0.28 x 50 = 14

Similarly, we take the number of white balls picked (18) and divide it by the total number of balls picked (25) to get the proportion of white balls in the tub. Then we multiply that proportion by the total number of balls in the tub (50) to get our estimate for the number of white balls in the tub.

18 / 25 = 0.72

0.72 x 50 = 36

This method of calculation makes sense because it uses the data we have (the number of orange and white balls picked) to estimate the overall makeup of the tub. By using the proportion of orange and white balls picked, we can make an educated guess about how many of each color ball are in the tub without seeing it.

However, it's important to note that this best estimate is not necessarily accurate. The real number of orange and white balls in the tub could be different. The method used here is a probability method, it's best estimate based on the sample data. The sample data is based on a random selection of 25 balls, and the number of orange or white balls that would be picked could vary depending on the random draw. The more samples we take, the more accurate our estimate would be.