Question

QUESTION 4 This semester, 40% of students are registered for a Sociology course; 30% are registered for a Chemistry course: 15% are registered for Economics and Sociology courses: 5% are registered for Economics and Chemistry courses, 10% are registered for Sociology and Chemistry courses. Only 10% of students are NOT registered for any Economics, Sociology, or Chemistry classes. 2% of students are registered for courses in all three What percentage of students are registered for an Economics class? (It may help to draw a Venn diagram) 38% O 42% O 44% 48%

Answer 1

Answer is 48%

Let P(S) = students registered for Sociology =40%

P(C)= students registered for Chemistry =30%

P(E) = students registered for Economics =x (unknown)

P(S∩E) =students registered for both Sociology and Economics = 15%

P(S∩C) =students registered for both Sociology and Chemistry = 10%

P (E∩C) = students registered for both Economics and Chemistry =5%

P(S ∩E ∩C) =students registered for all the three = 2%

P(S'∪E'∪C') =students who didn't register for any of the three courses =10%

P(S∪E∪C) =students registered for any of the three subjects = 1- P(S'∪E'∪C') { that is, % of Total students - % of students who didn't register for any course} = 100% -10% = 90%

P(S∪E∪C ) = P(S) + P(E) + P(C) - P(S∩E) - P(S∩C) - P(E∩C) +P(S∩E∩C)

90 =40 + x +30 - 15 - 10 - 5 +2

90 = x + 42

x = 48%