00:02
So we're given probability of a1 is equal to 0 .4.
00:04
We're given the probability of b1 given a1 is equal to 0 .6.
00:11
And the probability of b1 given a sub 2 is equal to 0 .7.
00:17
And we want to find the probability of a1 given b1.
00:24
And so let's make a little chart.
00:27
This is the easiest way.
00:28
We'll put a1, a2 here, and we know that these two will be complements, and b1, and b2 will be complements.
00:37
And we'll fill in the information we have.
00:40
First of all, we know that the probability of a1 is 0 .4, so that would be this column total.
00:48
And this intersection, the probability of b1 given a1, which we know is equal to 0 .6, comes from finding the probability of b1 and a1 divided by the probability of a1.
01:07
But we know what a1 is.
01:10
A1 is 0 .4.
01:13
Therefore, the probability of the intersection is 0 .4 times 0 .6 is 0 .24.
01:21
So that's this cell.
01:22
And that means that this probability must be 0 .16.
01:28
Now, using this one, because right now we don't know, well, actually, we do know one thing here...