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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