Sixteen students study Algebra, 21 study Biology, and there are 30 students in all. What is the probability that a student chosen at random studies Algebra or Biology?

Answer 1

In this problem, I'm assuming that there zero students studying neither Algebra nor Biology.

First, get the number of students(x) who are studying both Algebra and Biology:

16+21-x = 30

37-x = 30

x= 7

Then we have this Venn Diagram:

The famous formula to solve P(A or B):

P(A or B) = P(A) +P(B) -P(A and B)

P(A) = 16/30

P(B) =21/30

P(A and B) = 7/30

P(A or B) = 16/30 + 21/30 - 7/30 = 30/30 = 1

1. I hope you wrote the problem correctly and didn't miss anything.