00:01
So in this question, we are told to assume that we have two events, a and b, that are mutually exclusive.
00:07
And we're supposed to assume further that we know that the probability of event a occurring is 0 .3, and the probability of event b occurring is 0 .4.
00:23
Okay, so what we're asked in part a is to find out the probability of the intersection of the sets a and b.
00:30
And the answer to that is just that we need to understand what usually exclusive means, right? so if two sets or if two groups are mutually exclusive, that means that they share no elements, right? and since they tell us that a and b are mutually exclusive, that tells us that they can't occur at the same time.
00:49
So it means that this probability is going to be equal to zero, because there's no intersection between these two.
01:00
They don't happen at the same time.
01:02
Okay? now for part b, they want us to find the probability that a occurs if b is.
01:14
Occurs, okay? but following our logic from last time, let me try and fill out this formula.
01:22
So it's the probability of a intersection of v, all over the probability of b, right? problem is that our numerator ends up being zero.
01:33
So, means that this entire thing ends up being zero.
01:40
And part c, we see that a student is arguing that the concepts of mutually exclusive events and independent events are really the same.
01:49
And that if events are mutually exclusive, they must be independent.
01:52
And they're asking us if we agree with this statement, and we're supposed to use the probability information in this problem to justify our answer.
02:00
So, for starters, we need to say that no, we don't agree with this answer.
02:05
And to explain to you guys why it's no, we're going to go through the definition first, right? so mutually exclusive means that events can't happen at the same time.
02:16
However, independent events occur when one event remains unaffected by the current of another event, right? so we can definitely use the examples, sorry, the examples in this question, right? we can say that yes, they can occur.
02:38
So yes, these two are mutual exclusive, right? like one can occur after the other, but they can't happen at the same time.
02:46
But if we're going to look at an independent event, that would be the opposite...