# Crooked dice?

A pair of crooked 6 sided dice are rolled.

Each die has the following probabilities $$P(n)$$ of rolling the number $$n$$:

• $$P(1) = 1/2$$
• $$P(2) = 1/4$$
• $$P(3) = 1/8$$
• $$P(4) = 1/16$$
• $$P(5) = 1/32$$
• $$P(6) = 1/32$$

If the probability that they roll the same number is of the form $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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