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The probability that Julio will be assigned the same color for both sessions is 1/3.
Since there are three possible colors (Red, Yellow, Green) and participants are randomly assigned to each color in each session, there are a total of 3 x 3 = 9 possible outcomes for Julio.
Out of these 9 possible outcomes, there are 3 outcomes where Julio is assigned the same color for both sessions: (Red, Red), (Yellow, Yellow), and (Green, Green).
Therefore, the probability that Julio will be assigned the same color for both sessions is 3/9 = 1/3.