Question

Theoretical Probabilities of Repeated Events Quick Check
4 of 54 of 5 Items
Question
Julio is attending a summer camp. It has two sessions, and participants are divided into three groups: Red, Yellow, and Green. Participants will be randomly assigned to each color in each session. What is the probability that Julio will be assigned the same color for both sessions?(1 point)
Responses

13
Start Fraction 1 over 3 End Fraction

19
Start Fraction 1 over 9 End Fraction

12
Start Fraction 1 over 2 End Fraction

38
Start Fraction 3 over 8 End Fraction

Answer 1

To find the probability that Julio will be assigned the same color for both sessions, we can follow these steps:

1. **Identify the Total Colors**: There are three colors: Red, Yellow, and Green.

2. **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).

3. **Total Outcomes for Both Sessions**: Since each session has 3 colors, the total possible combinations for both sessions is:
\[
3 \times 3 = 9
\]

4. **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.

5. **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**.