Question

Example 3

he two In a class of 60 students, 46 passed Biology
and 42 passed Chemistry. Every student
ariable passed at least one of the two subjects. How
many students passed in both subjects?
Solution
Let U = students in the class
cps​

Answer 1

28 students passed in both subjects.

Explanation:

We solve this question treating each event as a Venn set.

I am going to say that:

Event A: Passed Biology.

Event B: Passed Chemistry.

46 passed Biology

This means that
`A = 46`

42 passed Chemistry.

This means that
`B = 42`

Every student passed at least one of the two subjects.

This means that
`A \cup B = 60`

How many students passed in both subjects?

This is:

`A \cap B = A + B - A \cup B`

From the values we have above

`A \cap B = 46 + 42 - 60 = 28`

28 students passed in both subjects.