# Pirate's Booty

There are three caskets of treasure. The first casket contains $$3$$ gold coins, the second casket contains $$2$$ gold coins and $$2$$ bronze coins, and the third casket contains $$2$$ gold coins and $$1$$ silver coin. You choose one casket at random and draw a coin from it. The probability that the coin you drew is gold has the value $$\frac {a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a+b$$?

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