Second roll beats the first

You roll a fair $6$ -sided die twice. What is the probability that the first roll is strictly less than the second?

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Of $36$ ordered outcomes, how many are ties? Split the rest by symmetry.
$6$ ties leave $30$ split evenly: $15$ each, so $\tfrac{15}{36}=\tfrac{5}{12}$ .

Answer

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0.4167 (± 0.005)

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Asked at: Optiver, IMC