Answer:
the probability that one student studies French but not German and the other student studies German but not French is 0.
Explanation:
Given the information provided:
- The total number of students in the class is 30.
- 8 students study French.
- 11 students study German.
- 9 students study both French and German.
- 2 students do not study either subject.
To calculate the probability, we need to determine the number of students who meet the criteria and divide it by the total number of possible outcomes.
1. Number of students who study French but not German:
- We know that 8 students study French, but 9 students study both French and German.
- Therefore, the number of students who study French but not German is 8 - 9 = -1. However, the number of students cannot be negative, so we consider it as 0.
2. Number of students who study German but not French:
- We know that 11 students study German, but 9 students study both French and German.
- Therefore, the number of students who study German but not French is 11 - 9 = 2.
To calculate the probability, we divide the number of favorable outcomes (students who meet the criteria) by the total number of possible outcomes (total number of students):
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (0 students who study French but not German * 2 students who study German but not French) / (30 total students * 29 remaining students to choose from)
Probability = 0 / (30 * 29)
Therefore, the probability that one student studies French but not German and the other student studies German but not French is 0.