To find the probability that Julio will be assigned the same color for both sessions, we first note that there are three color groups: Red, Yellow, and Green.
In each session, Julio can be assigned to any one of these three colors. This means that the total number of possible outcomes for his color assignments across the two sessions is:
- For Session 1, he has 3 choices (Red, Yellow, or Green).
- For Session 2, he also has 3 choices (Red, Yellow, or Green).
Therefore, the total number of combinations of colors for both sessions is:
\[ 3 \text{ (choices for Session 1)} \times 3 \text{ (choices for Session 2)} = 9 \text{ total outcomes}. \]
Next, we consider the favorable outcomes, which are the instances in which Julio is assigned the same color in both sessions. The possible favorable outcomes are:
- Red in Session 1 and Red in Session 2
- Yellow in Session 1 and Yellow in Session 2
- Green in Session 1 and Green in Session 2
This gives us 3 favorable outcomes.
To find the probability that Julio will be assigned the same color in both sessions, we use the formula for probability:
\[ P(\text{same color}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{9} = \frac{1}{3}. \]
Thus, the probability that Julio will be assigned the same color for both sessions is:
\[ \frac{1}{3}. \]
So the answer is 1/3.