To determine the probability that Julio will be assigned the same color for both sessions, we first note that there are three possible colors: Red, Yellow, and Green.
In the first session, Julio can be assigned to any of the three colors. After he has been assigned a color in the first session, he can still be assigned any of the three colors in the second session.
Now, we want to find the probability that Julio is assigned the same color in both sessions.
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The total number of outcomes for the color assignments across both sessions is:
- For the first session: 3 options (Red, Yellow, Green)
- For the second session: 3 options (Red, Yellow, Green) Thus, the total number of outcomes for both sessions = \(3 \times 3 = 9\).
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The number of favorable outcomes where Julio is assigned the same color in both sessions:
- If he is assigned Red for both sessions, that counts as one outcome.
- If he is assigned Yellow for both sessions, that counts as another outcome.
- If he is assigned Green for both sessions, that counts as another outcome. Thus, the number of favorable outcomes = 3 (one for each color).
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Therefore, the probability that Julio is assigned the same color for both sessions is given by the ratio of favorable outcomes to total outcomes: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{9} = \frac{1}{3}. \]
Thus, the probability that Julio will be assigned the same color for both sessions is \(\frac{1}{3}\).
The answer is \(\boxed{\frac{1}{3}}\).