Out of 200 grade 11 students 160 passes maths 150 passes science and 10 did not pass anything i) represent the following in a venn diagram ii) find the number of students who a) passed both math and science b) passes only maths c) passed only science

Total students = (Students who passed at least one subject) + (Students who passed nothing)
200 = (Students who passed at least one subject) + 10
Students who passed at least one subject = 200 - 10 = 190

We use the formula for the union of two sets: |M U S| = |M| + |S| - |M ∩ S| Where |M U S| is the number of students who passed at least one subject, |M| is the number who passed Maths, |S| is the number who passed Science, and |M ∩ S| is the number who passed both.
190 = 160 + 150 - |M ∩ S|
190 = 310 - |M ∩ S| |M ∩ S| = 310 - 190 |M ∩ S| = 120

Students who passed only Maths = (Students who passed Maths) - (Students who passed both Maths and Science)
Only Maths = 160 - 120
Only Maths = 40

Students who passed only Science = (Students who passed Science) - (Students who passed both Maths and Science)
Only Science = 150 - 120
Only Science = 30

i) Represent the following in a Venn diagram
Let M be the set of students who passed Maths and S be the set of students who passed Science.
The Venn diagram would show two overlapping circles.

• The overlapping region (intersection M ∩ S) contains 120 students (passed both).
• The part of circle M that does not overlap with S contains 40 students (passed only Maths).
• The part of circle S that does not overlap with M contains 30 students (passed only Science).
• Outside both circles, there are 10 students (passed nothing). (Check: 40 + 120 + 30 + 10 = 200 total students)

ii) Find the number of students who

a) passed both math and science
From Step 2:
The number of students who passed both Maths and Science is 120.

b) passed only maths
From Step 3:
The number of students who passed only Maths is 40.

c) passed only science
From Step 4:
The number of students who passed only Science is 30.