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Discrete Mathematics Level 3

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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