Hello, hven191!

This doesn't require any fancy formulas . . .

The probability for students at a certain university

to pass Mathematics and Economics are 3/7 and 5/7 respectively.

One student failed both subjects and four students passed both subjects.

Find the number of students who took the test. Make a Venn diagram of the students who passed. Code:

*---------------------------------------*
| |
| *-----------------------* |
| | Math | |
| | only *---------------+-------* |
| | M | Both | | |
| | | 4 | | |
| | | | | |
| *-------+---------------* Eco | |
| | E only | |
| *-----------------------* |
| Neither 1 |
*---------------------------------------*

Let = number of students that passed Math only.

Let = number of students that passed Economics only.

We know there are 4 that passed both, and 1 that failed both.

The total number of students is: .

The number of students that passed Math is: .

The probability that a student passed Math is

We have: .

The number of students that passed Economics is

The probability that a student passes Economics is

We have: .

Substitute into [1]: .

Therefore, the number of students is: .