One of the probability quizzes asks:
A high school offers courses in French and in Spanish (and only those two languages). A sample of students from the school were asked which language courses they enrolled in. 60% of the students responded that they took French, 30% of the students responded that they took Spanish, and 20% of the students responded that they did not enroll in any language course.
If a student is randomly chosen from among the students surveyed, what is the probability that the student enrolled in the French course, but not in Spanish course?
My thought was that the answer would be 52%, but they disagree:
Correct answer: 0.5
If 20% of students are not in a language course, then 80% of students are in a language course. 60% are in French and 30% are in Spanish, so that means that 10% must be enrolled in both. Then 50% of students are enrolled in the French course, but not the Spanish course. Thus, the probability that a student would be enrolled in the French course, but not the Spanish course, is 0.5
My thinking is that there's no way to tell, because it's possible that all 30% of the Spanish students are also French students.
Or, if they mean those surveyed responded that they took ONLY Spanish or ONLY French, then that would mean there's a 60% chance to be a French student and a 30% chance to be a Spanish student, and the chances of being ONLY a French OR Spanish student would be 60% + 30% - 60*30% which is 72%, leaving 8% of the 80% of students taking a foreign language to take both languages. So, students taking french (60%) minus students taking both (8%) is 52%.