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There are 50 small balls in a tub. Some balls are white and some are 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, 7 orange balls and 18 white balls were picked. What is the best estimate you can give for the number of orange balls and the number of white balls in the tub? Describe how to calculate this best estimate, and explain your method of calculation makes sense in a way that a seventh grader might understand. Is your best estimate necessarily accurate? Why or why not?

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  1. Based on the sampling of 25, we can estimate that the chance of drawing an orange ball is 7/25.
    Let's say we did a sampling of 50. This tells us that, since 50 is 2 x 25, we could estimate that the chance of drawing an orange ball is then 14/50.

    Some students might note that we are returning the balls each time, so it doesn't really represent the actual 50 balls that are in the bag. So we can also think about it this way: there appear to be 18 white balls for every 7 orange balls. 18+7 =25. So we could double these values and estimate that there are 36 white balls for every 14 orange balls. 36 +14=50.

    Lastly, we can note that a best estimate isn't necessarily correct because we need many more trials for accuracy. While not probable, it is possible that there is 1 orange ball and 49 white balls in the tub!

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