To find the probability that Julio will be assigned the same color for both sessions, we first need to determine the total possible outcomes and the favorable outcomes.
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Total outcomes: Since there are three groups (Red, Yellow, Green), and Julio can be assigned to any of these groups independently in both sessions, the total number of possible outcomes for the two sessions is \(3 \times 3 = 9\).
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Favorable outcomes: The favorable outcomes where Julio is assigned the same color for both sessions are:
- Red in both sessions
- Yellow in both sessions
- Green in both sessions
This gives us a total of 3 favorable outcomes (Red, Yellow, Green).
- Calculating the probability: The probability \(P\) that Julio is assigned the same color for both sessions is given by the ratio of the number of favorable outcomes to the total outcomes:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{9} = \frac{1}{3} \]
Thus, the probability that Julio will be assigned the same color for both sessions is \(\frac{1}{3}\).
So, the correct response is:
\(\frac{1}{3}\)