# Answer on Statistics and Probability Question for Shashi

Question #6787

In order to test a dice for fairness, it is thrown repeatedly until a 6 appears. How many throws will you need in order to start suspecting that the dice is probably biased? (So, how many throws will you need with no 6 till you will start believing that there is a problem with the dice?

Expert's answer

Let's assume that normal dice has uniformly distributed sides appearance, i.e.

P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = 1/6,

so the sequence

n1, n2, n3, ... , nN

of numbers of throws before 6 appearing should be uniformly distributed with expected value 1/6. We can use chi-square test to check the hypotesis that the dice isn't biased. The number of throws will depend on the chosen significance level and the dice - we need to throw a dice until the data will not convince us that the dice is biased.

P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = 1/6,

so the sequence

n1, n2, n3, ... , nN

of numbers of throws before 6 appearing should be uniformly distributed with expected value 1/6. We can use chi-square test to check the hypotesis that the dice isn't biased. The number of throws will depend on the chosen significance level and the dice - we need to throw a dice until the data will not convince us that the dice is biased.

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