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# Probability

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Meyer rolls two fair, ordinary dice with the numbers 1,2,3,4,5,6 on their sides. What is the probability that neither of the dice shows a square number?

Jan 31, 2022

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There are $$36$$ possible outcomes ($$6$$ for the first roll and $$6$$ for the second roll).

The only square numbers in the list are $$1$$ and $$4$$.

If we don't want either of these, there is $$4$$ sucsessful options for the first role and $$4$$ sucsessful options for the second roll. This means that there is $$16$$ succsessful outcomes, out of the $$36$$ total outcomes, meaning that the answer is $$16\over 36$$, which can be simplified to $$\color{brown}\boxed{4\over9}$$

Jan 31, 2022