Question

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In a college dorm 40 students are math majors, 14 are English majors, and 8 are majoring in both math and English. There are 70 additional students that are neither English nor math majors.

1.Are the math and English majors mutual?

2. Are the math and English majors dependent or independent?

Answer 1

Total number of students = 70+ 40 + 14 - 8 = 116

Let A denote the event nath major and B denote the event English major

1.

Since , A and B are not mutually exclusive

2. = 0.0690

P(A) = ;

P(B) =

P(A) x P(B) =

So we see that

So A and B are not independent.