Question

You are given: Students must take at least 2 courses out of Art, History, and Science. 60% of the students take Art. 80% of the students take History. 70% of the students take Science. What is the proportion of the students who take all 3 courses?

Answer 1

Answer:

0.10 or 10%

Step-by-step explanation:

Since each student must take at least 2 courses, if no student took all three courses, the sum of the percentages would total 200% (counting each student twice). Therefore, the proportion of students taking all three courses is the difference between the sum of all percentages and 200%:

$P(3) = 60\%+80\%+70\%-200\%\\P(3) = 10\%$

0.10 or 10% of the students take all 3 courses.