Fabio's Can Dilemma

Chef Fabio went to the store and bought 2 cans of beans, 2 cans of tomatoes, and 2 cans of tuna, all of which were the same shape and size. On his way home, it rained hard and the labels became soaked and fell off the cans. He wants to make a dish using one can of each type, and begins to open the cans one at a time. The expected number of cans he will have to open to get one can of each type can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?

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