Rolling die

Mabel has a standard 4-sided die with sides numbered 1 through 4. Each time Mabel rolls the die she writes down the number she rolls. After some number of rolls, the total of the numbers Mabel has written down is 5. We know that she must have rolled the dice at least twice. The expected number of times Mabel rolled the die can be expressed as \(2+\frac{a}{b}\) where \(a\) and \(b\) are positive coprime integers. What is \(a+b \)?

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