What is the probability that an F2 seed chosen at random from among the yellow seeds will breed true when

Just as you've laid it out in your question. There is 1 YY (the only seed that will breed true for Yellow). There are 2 Yy, which are Y, but will not breed true for yellow, and there's 1 yy (which I'm guessing is green, and will only breed true for that color. Since that seed won't be included in with the seeds that are yellow, there are only 3 to choose from.

So that's a total of 3 yellow seeds, and out of those 3, only one is YY (true breeding for yellow) Your chance of picking up one seed and having it be YY (true breeding for yellow) is 1 in 3, or 33.3%