00:01
A and b are independent, there are two events, and we want to show that if they are independent, we have that the complements are also independent.
00:14
To show this, we need to use the formula like we want to show that if you put the intersection of these two events, we want to check that this here is also the multiplicatory.
00:30
If they are independent.
00:33
So we want to show this.
00:34
So let's go from here and we will get there.
00:39
So first we can open this here as 1 minus, because this is the complement.
00:46
So 1 minus the probability of a union of b.
00:53
And after we got this, we just need to open this.
00:58
What is this here? is 1 minus and i'm going to put pa just open the union so the union of two events is the probability of a plus the probability of b in this case minus the probability of the intersection now that we have this let me just multiply the minus term that we have here to just open everything so we have like a 1 minus pa minus p b and now we have plus pa intersection with b...