00:01
So we're given a few probabilities.
00:02
We know the probability of a1 is equal to 0 .8.
00:05
The probability of b1 given a1 is equal to 0 .6.
00:12
And the probability of b1 given a sub 2, another conditional, is equal to 0 .2.
00:19
And we want to end up finding the probability of a1 given b1.
00:26
Now, so that's what we want to find.
00:29
Let's draw a chart of the information we're given.
00:33
And so we know a1 and a2 are going to be complementary events.
00:38
And here's b1 and b2 and likewise they're complementary events.
00:43
And we know that a1 has a probability of .8.
00:51
So the probability of a sub 2 will be .2 and they add up to 1.
00:57
And we know that this conditional is 0 .6.
01:03
So where do we get that conditional? that conditional comes from taking the probability of b1 and a1 divided by the probability of a1.
01:16
And we know that that has to equal 0 .6 because that's the definition of that conditional.
01:22
However, we know this probability.
01:24
This probability is 0 .8.
01:28
So the intersection, this cell right here, of b1 and a1, is 0 .8 times 0 .6, which is 0 .48.
01:36
So this must be a probability of 0 .32.
01:41
Now, let's see what else we know...