Answer: I disagree. The answer is 1/4
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Reason:
Ari hasn't considered the case of "red and yellow" which is almost identical to "yellow and red".
It helps to lay out a two by two table. Along the rows and columns, you'll have "red" and "yellow". See below.
Then inside the table are the list of all outcomes in the form (x,y) where x is the horizontal component along the columns, and y is the vertical component along the rows.
Example: if x = red and y = red, then we have the outcome (x,y) = (red, red)
As the table shows, we have 4 outcomes. Therefore the probability of getting two yellows is 1/4
Technically the (red, yellow) = (yellow, red) since ultimately order doesn't matter in this case. For some probability problems, order will matter. But again, order doesn't matter here and it means that we can treat these two situations the same. So I can see why Ari thinks there are only three outcomes.
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Here's another way to look at it:
The probability of landing on yellow is 1/2 assuming red and yellow are equally likely.
This means the probability of two yellow in a row is (1/2)*(1/2) = 1/4
Each is spin is independent of any other.
