00:01
Let's look at what we're given.
00:01
We're given that the probability of a given b intersect c is equal to one -fourth.
00:12
We're given that the probability of b given c already occurred is one -third, and we're given the probability of c is equal to one -half.
00:23
And we know that we want to end up finding the probability of a complement intersected with b, intersected with c.
00:32
Now let's look at what that is in the venn diagram.
00:37
So here is a, here is b, and here is c.
00:43
Whoops, and that c is supposed to stay in there.
00:45
So why don't we just kind of erase this and make that a little bit bigger so that my diagram is not messed up.
00:53
There we go.
00:55
And we know that this, i'll mark it in red, is equivalent to a, intersect b, intersect c.
01:05
Now, we want to find the complement of a.
01:11
Well, outside of a, that also intersects b and c is this region.
01:17
This is what we want.
01:19
Okay, so that's what we want.
01:21
So we know that the sum of these two, of this and a intersect b intersect c will end up equaling the intersection of a, excuse me, of b and c.
01:36
So these two regions will be the intersection of b and c.
01:40
So let's start finding out what we need to know.
01:44
So our goal is basically to find either this or this.
01:48
So from this statement, we know that this is equal to the intersection b, and c divided by the probability of c.
02:00
That's the definition of a conditional probability...