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# Probability

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Amaya and Bo each roll a fair, ordinary six-sided die with the numbers 1,2,3,4,5,6 on the sides. What is the probability that Amaya rolls a number at least two than Bo?  Enter your answer as a fraction in simplified form.

Feb 1, 2022

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There are a total of $$36$$ possibilities ($$6$$ for the first, $$6$$ for the second). The only way the two numbers will be different is if they are the same, or if they differ by one.

There are $$6$$ possible ways to roll the same number twice, and there is $$10$$ ways to roll two numbers that differ by one.

This means that the probability is $$\color{brown}\boxed {5\over 9}$$

Feb 1, 2022