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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