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A drawer contains black socks and white socks.

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A drawer contains black socks and white socks. 80% of the socks are white socks. A number generator simulates randomly selecting 10 socks from the drawer. The number generator is used 10 times and the number of white socks in each trial is shown in the dot plot.

Which description is correct about the number generator being fair or not?

The number generator is not fair. The correct percentage of white socks was not chosen at all.

The number generator is not fair. In three experiments, it picked white socks 90% of the time.

The number generator is fair. It picked white socks half of the time.

The number generator is fair. It picked the approximate percentage of white socks most of the time.

May 8, 2019

#1
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Let's start by eliminating some choices. A and C can't be correct. For A, 8 socks were chosen 4 times, which means that the proportion was met at least once. Therefore, because the reasoning is invalid, A can't be the right answer. For C, white socks were picked far more often than half the time. Because of this we can eliminate C as a possible answer, leaving only B and D.

Think this one through. We know that 80% of the socks are white socks, so it is fair to say that there are 8 white socks out of 10 total socks. It appears this trial was run 10 times. I think a regular, "add and divide" average should suffice here. So $$\frac{7 \times 3 + 8 \times 4 + 9 \times 3}{10}$$ is the long form of our average. The convinient part is that this equals exactly 8, so if we assume that there were 10 socks, the average perfectly matches. Therefore, we can say that D is the right answer. The reason behind C is true, but the 9-sock outcomes were counterbalanced by 3 seven-sock outcomes.

May 9, 2019
#2
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Thanks, helperid   !!!!

CPhill  May 9, 2019
#3
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There can't be 10 socks helperid

Guest May 9, 2019