Suppose there are 20 coins in a bag, 14 of which are fair, (i.e., one side shows heads and the other tails), 4 of which show heads on both sides and 2 of which show tails on both sides. (The coins are otherwise identical to the touch.)

A coin is chosen from the bag at random, and one of its sides, again chosen at random, is observed. Given that the side observed shows heads, what is the probability that the other side of this coin also shows heads?

If the probability is $$\dfrac{a}{b},$$ where $$a$$ and $$b$$ are positive coprime integers, then find $$a + b.$$

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