Question

In a group of 40 students, 22 study Economics, 25 study Law, and 3 study neither of these subjects. Determine the probability that a randomly chosen student studies:

1. Both Economics and Law
2. At Least one of these subjects
3. Economics given that he or she studies Law


I really don't understand how to calculuate the 3rd one.

Answer 1

there are 47 places in the two classes that are filled by 37 students
... 3 of the 40 students are in neither class

if B is the students in both classes
... 22 + 25 - B = 37

1. 10 of 40

2. 37 of 40 students in at least one class

3. 25 in Law ... 10 in both ... 10 of 25