Alexane has four chocolate fair coins.

She flips all the coins and eats those that fall on head.

She flips the coins not eaten (those that fell on tail) a second time and eats those that fall on head.

What is the probability that Alexane has eaten more than 2 coins?

If the probability can be expressed as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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