00:01
Hello, so let's look at the information we have here.
00:06
So we have the probability of a probability, the second probability of a to be 0 .2, that of b is 0 .6.
00:23
There we have, let's a second, this is a second.
00:35
This is 0 .25.
00:43
So let's look at the first thing we want to find.
00:45
So first we want to find p, i'm sorry, the probability of a intersection of b.
00:58
So because these events are interdependent, we're going to start off with the general expression of a or b, which is a union b that is given by b plus that and the intersection b.
01:29
This is the general expression for probability of a or b.
01:37
So you realize that if you want to find this, which is the first question, and p.
01:47
Probability of a intercession b it's going to be equal to probability of a probability of b minus probability of a or b right but we don't have probability of a or b but this expression is another general expression for probability of a complement intercession b complement that is the same as probability of a union b complement so that is 0.
02:43
So from this we can also write that probability of a complement is the same as 1 minus the probability of a union b so probability of a and b if you rearrange this is going to be one minus probability of a of a, we're going to have 1 minus 0 .25, it will be 0 .75.
03:28
And so finally, i'll find the probability of a intersection b, which is equal to the probability of a, that is 0 .2.
03:45
So you'll put it in back into this formula here, right? so we have 0 .2 plus 0 .6 minus 0 .75.
03:57
So this is going to give 0 .8.
04:07
So that's going to be 0 .05.
04:13
Let's look at the second part of the question, which is the probability of a, intersection b complement, union probability of a, complement, intersection b complement.
04:35
So you can see this is the same as the probability of a, intersection b, complement plus p, probability of a, of a intercession a complement interstation b complement so let's see but we don't have so we have this guy or we don't have the expression on the left so let's look at a term on the left so for probability of a intercession b complement that is going to be the same as probability of a minus the probability of a intersection b okay so we can easily get a substitution for that, right? because we have the probability of 8.
05:38
So this is 0 .2, oops, just 2.
05:41
This is 0 .2 minus 0 .05.
05:58
That's going to be 0 .15.
06:03
So now, finally, we can have into 05 plus, we have that, right? that's 0 .25, 25.
06:23
5 and so we get 0 .30.
06:31
Okay, let's see whether, just a second.
06:53
Let's just point two.
06:59
Let me double check my calculation here...