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A die was rolled 600 times, and the six came up 117 times…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A die was rolled 600 times, and the six came up 117 times. A fair die gives 100 sixes on average. Is 117 unusual? Simulate 20 000 experiments of 600 rolls of a fair die (use rng.binomial(600, 1/6, size=20000), which gives the number of sixes of each experiment), and find the share of the experiments with 117 sixes or more.
The worked solution
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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. rng.binomial(600, 1/6, size=20000) is the number of sixes in each of 20 000 experiments. The share with 117 or more tells how often a fair die gives such a result.
Check. The spread is about , and 117 is spreads above 100. About 3.6 percent of the experiments with a fair die give 117 or more.
Answer: about 3.6 percent. A result like 117 is a little unusual, but a fair die gives it in about one experiment in 28. It is not strong evidence that the die is unfair. If it were 130 sixes, we would be sure.
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