00:01
In this question, we're given that probability of b given a is greater than probability of b.
00:07
Now, what is probability of b given a? this is conditional probability.
00:17
That is the probability of b given that a has already occurred.
00:21
Now, using bayes theorem, probability of b given a is probability of b in a set a over probability of a.
00:29
And we're given that is greater than probability of b.
00:32
So we want to show probability of b complement given a is less than probability of b complement.
00:40
So let's start with this.
00:42
Probability of b complement given a.
00:46
So by definition, this will be probability of b complement intersect with a over probability of a.
00:55
Now let's draw the v diagram.
00:59
So this is a and this is b.
01:02
Now b complements everything outside a and intercept with a, and that will be this part only.
01:09
So basically this is probability of a only.
01:14
So what i will do is i'll take probability of a minus of probability of this middle part here, which is a in the set b.
01:25
Okay, so this is how it will look like.
01:28
It will be probability of a minus probability of a in the set b over probability of a.
01:35
Of a...