To find the probability that Julio will be assigned the same color for both sessions, we can follow these steps:
-
Identify the Total Colors: There are three colors: Red, Yellow, and Green.
-
Calculate the Probability of Assignments:
- For the first session, Julio can be assigned any of the 3 colors (Red, Yellow, or Green).
- For the second session, to be assigned the same color, he has only 1 favorable outcome (the same color he received in the first session).
-
Total Outcomes for Both Sessions: Since each session has 3 colors, the total possible combinations for both sessions is: \[ 3 \times 3 = 9 \]
-
Favorable Outcomes: There are 3 favorable outcomes (Red/Red, Yellow/Yellow, Green/Green), which correspond to Julio being assigned the same color in both sessions.
-
Calculate Probability: The probability that Julio is assigned the same color in both sessions is given by the ratio of favorable outcomes to total outcomes: \[ P(\text{same color}) = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{3}{9} = \frac{1}{3} \]
Therefore, the probability that Julio will be assigned the same color for both sessions is \( \frac{1}{3} \).
The correct response is: Start Fraction 1 over 3 End Fraction.