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 ab, where a and b are coprime positive integers. What is the value of a+b?

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probability has to be <1. It can't be a product of two integers.

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