After getting trounced by your little brother in a children's game, you suspect the die he gave you to roll may be unfair. To check, you roll it 48 times, recording the number of times each face appears. Do these results cast doubt on the die is fairness

The results are

Face     Count         Face          Count

1               6                  4                9

2              12                 5                5

3              8                 6               20

These results are not fair, because they clearly shows that the dice was tricked. We deduct this by observing that he obtained the face 6, 20 times out of 48, which represents 42% of chances to get that result.

Now, a fair dice must have equal probabilities per side, or an approximation to that at least. In this case, we don't have such equality.

So, next time your little brother roll the dice, we probably will get 6.

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