Toss It Til You're Convinced!

You have an unfair coin. The probability it will land on heads is \( \dfrac23\).

The expected value for the number of coin flips it will take to get 3 heads in a row can be expressed as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

What is \(a+b\)?


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