Coins in Caskets

Discrete Mathematics Level pending

Suppose there are three caskets. Casket 1 contains \(2\) gold coins, Casket 2 contains \(1\) gold and \(1\) silver coin, and Casket 3 contains \(2\) silver coins. Suppose you choose one casket at random and draw a coin. If the coin is gold, the probability that the second coin in the casket is gold can be written as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

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