00:01
For this problem to begin, we know that the number of students who like mathematics is equal to 60.
00:07
The number of students who like science, i'll call that n of s, is equal to 45.
00:14
And the number of students who like both mathematics and science is equal to 30.
00:20
For part a, we're asked how many students like either mathematics or science or both.
00:26
So that is n of m or s, we could call it, which we calculate using the inclusion -exclusion principle.
00:34
So that's n of m plus n of s minus n of m and s.
00:42
We need to subtract off the number of individuals in the intersection to avoid over counting.
00:47
So we'd have 60 plus 45 minus 30 for a result of 75.
00:51
Then for part b, we're asked how many students do not like either mathematics or science.
00:59
So the number of students in m complement and s complement, we can think of as the number of students in the complement of m or s, which is going to be equal to the total number of students in the sample.
01:23
I'll call that n of omega, omega representing our sample space, minus the number of students in m or s...