00:01
In a class of size 100, we are told that the number of students that took math is 54.
00:07
The number that took history is 69, and the number that took both math and history is 35.
00:16
Now these can all be converted to probabilities by dividing by the total size of the class, so that's .54, .69, and .35.
00:40
Now for part a, we are asked for the probability that are randomly selected.
00:44
Selected student.
00:46
So history or mathematics.
00:49
So that's the probability of m, union, h.
00:56
And using probability theory, this is equal to the probability of m plus the probability of h minus the probability of h intersect m, and this is equal to .88.
01:28
So that's the probability of having taken math or history.
01:34
For b, we want the probability that the randomly selected student took neither mathematics nor history.
01:43
So that's the probability of not taking math, intersected with not taking history.
01:52
And this is equal to the probability of m union h complement, which is 1 minus the probability of m union h.
02:08
And we've just solved for the second term in part a, so this is 1 minus .88...