# One die and 1, 2 or 3 coins

A fair die is tossed.
If the die lands on 1, 2 or 3, then 3 fair coins are tossed.
If the die lands on 4 or 5, then 2 fair coins are tossed.
If the die lands on 6, then 1 fair coin is tossed.

Given that the resulting coin tosses produced no tails, what is the probability that the die landed on 6?

The probability can be expressed as $$\dfrac ab$$ for coprime positive integers $$a$$ and $$b$$, find the value of $$a+b$$.

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