Explanation of Venn-Diag answer, plz: each of 80 is taking either algebra or pre-calc

[Diego749]

Can someone help us with the problem below, the explanation is even more confusing to us, I think the answer should be 1/16 while my wife feels it should be 1/5, both answers which are not options , we appreciate all your help

Question 11 CORRECT​

There are 80 students in a school. Each student is taking either algebra or pre-calculus. There are 60 students in the algebra class. If 15 students are taking both algebra and pre-calculus, what is the probability that a randomly selected student is taking pre-calculus but not algebra?

B​
C​
D​

[COLOR=#003300 !important]Question 11 Explanation:
The correct answer is (A). We can set up a Venn diagram to help us determine the number of students taking pre-calculus but not algebra.

The number of students taking algebra but not pre-calculus = 45
We can figure out the number of students taking pre-calculus but not algebra (x) as follows:
45 + 15 + x = 80
x = 20
Therefore, the probability that a student is taking pre-calculus but not algebra is:

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[mmm4444bot]

Do you agree this ratio is the requested probability:

[Number of students taking precalculus only] / [Total students]

The Venn Diagram helps us reason out the number of students taking only precalculus.

Think of the Venn Diagram as two giant circles drawn on the gym floor. Each of the 80 students will take a position somewhere on the floor, according to their math class(es).

The circle on the left (labeled A for Algebra) contains all of the algebra students. The circle on the right (labeled P for Precalculus) contains all of the precalculus students.

But look! Part of circle A overlaps circle P. That region is for the students who are taking both classes because that area belongs to each circle.

We're told that 15 students take both classes, so they are standing in the overlap region.

We're told that a total of 60 students take algebra.

60 - 15 = 45

This difference shows how many of the 60 algebra students are not also taking precalculus.

Those 45 students take their position in the part of circle A that does not overlap.

The remaining students take their position in the part of circle P that does not overlap; those are the students who are not taking algebra (i.e., the ones who are taking only precalculus). How many?

60 students out of 80 are already in position, so that leaves 20 students remaining for the precalculus-only region.

[Number of students taking precalculus only] / [Total students] = 20/80