The Four Chocolate Coins

Probability Level 4

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 $a+b$ .