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How often will a die come up "4"? How likely is it to rain tomorrow? Probability is one of the most powerful frameworks for modeling the world around us.

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A fair 6-sided die is rolled twice. The probability that the second roll is strictly less than the first roll can be written as \(\frac{a}{b}\), where \(a\) and \(b\) are positive, coprime integers. What is the value of \(a+b\)?

**Details and assumptions**

The **roll of a dice** refers to the value on the top face of the dice.

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**same result** can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?

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