Please answer using proper notation and 4 decimal places. There are 89 students

Question

Please answer using proper notation and 4 decimal places.

There are 89 students in a volunteer group for majors in math, statistics, or actuarial science. Thirteen students have a double-major in math and statistics. Twelve students have a double major in math and actuarial science. Thirteen students have a double major in statistics and actuarial science. There are 9 students doing a triple major. Thirty-nine students are majoring in at least statistics, and forty-four are majoring in at least actuarial science. How many students are majoring in at least mathematics?

Explanation / Answer

Let M shows the major maths, S shows the major statistics and A shows the major acturail science, So we have

n(M or S or A) = 89

n(M and S) = 13

n(M and A) =12

n(S and A) = 13

n(M and A and S) = 9

n(S) = 39

n(A) = 44

and we need to find n(M)=??

Now

n(M or S or A) = n(M) + n(A) + n(S) - n(M and S) - n(M and A) - n(S and A) + n (M and S and A)

89 = 39+44+n(M) - 13 -12- 13 + 9

n(M) = 35

Hence, at least 35 students are majpring in at least mathematics.

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