The Four Chocolate Coins

Probability Level 3

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 ab \dfrac ab, where aa and bb are coprime positive integers, find a+ba+b.

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