00:01
Let's use set notation to represent the probabilities, where p of a represents the probability of event a, p of b represents the probability of event b, and p of a, b as such, represents the probability of the intersection of events a and b.
00:22
So we're given that p of a is one -third, p of b is one -third, and p of a intersecting with b is one -tenth.
00:42
So we can calculate the probabilities you've mentioned.
00:49
So number one, p of b prime represents the probability of the complement of event b, which is the probability that event b does not occur, so that would be one minus p of b, which would be one minus one -third, which equals two -thirds.
01:11
Secondly, p of a, u, b represents the probability of the union of event a and the complement of event b, which is the probability that either event a occurs or event b does not occur, or both.
01:30
So this would be one -third plus two -thirds minus one -tenth, which would be ten over thirty plus twenty over thirty minus three over thirty, which equals nine -tenths overall...