00:01
Question we're assuming this table and in item a we want to compute what is the probability that she will receive mail on monday so let's say that this event is the same as same monday mail on monday is the same as this so here here because the probability that we have is that to receive mail mail if she got like accepted or like to receive mail if she got rejected so in this case i have two options.
00:31
I could have the option that she got the mail.
00:33
So let's say she got the mail on monday and she was accepted.
00:43
Or i could have the second option, which is that she got mail monday, but she was rejected.
00:51
So we have these two things to consider.
00:55
So the way that we compute this, the first one, is the same as using the probability of like mail on monday, given that she was accepted, so let me put like this, times the probability of being accepted.
01:12
And for the second one, we can do the same thing, the probability of getting mail on monday, given that she was rejected, times the probability of getting rejected.
01:26
We say that this thing is the total probability.
01:34
So now we just need to plug the information that we have.
01:38
So for example, she will receive mail on monday, given she was accepted as equals to 015 and the probability of being accepted 0 .6, the probability of getting a mail on monday and given that she was rejected 0 .05 and the probability of being rejected is 1 minus the probability of being accepted.
01:59
So in this case is 0 .4.
02:02
So here what we are going to have is 0 .11 as the answer for item a.
02:10
For item b what we have to compute is the probability here that she will receive like a mail on tuesday.
02:18
So let's see like this, tuesday.
02:23
And considering that she did not get anything like on monday.
02:28
So let's see like this, like this, given that she got, she did not get any email on monday.
02:39
So we have this, right? so again, because this is a conditional probability, what we should do is compute the intersection between these two.
02:50
So she got the mail on tuesday and she did not receive any mail on monday.
02:58
Then divide this by the probability of, in this case, not getting any mail on monday.
03:08
So now the thing here is, if for example, the probability that she would like get mail on monday or in tuesday and not get any mail on monday here, is the same as saying that she got like her just mail on tuesday.
03:31
So this means that in the end, what we need to compute here is only the probability of tuesday here.
03:42
So let me put here like the from here to here.
03:46
So what we have is the probability of tuesday in the numerator, divided by the probability of not monday, which is the same as not one minus the probability of receiving.
03:56
Email on monday that we already have from the previous question.
04:04
So using the same idea here to compute the tuesday, what we have is the option that she could get accepted or not.
04:11
So we are going to use the same formula here, but like consider tuesday instead of monday.
04:18
So basically the probability that she will receive a mail on tuesday if she got accepted 0 .20 times the probability of being accepted and the probability of receiving a mail on tuesday, if she was rejected, is 0 .10 times the probability of being rejected.
04:38
And 1 minus the probability of receiving mail on monday, which is 1 minus 0 .11.
04:44
So this here is the same as 0 .16, 1 minus 0 .9 here.
04:50
So let me just put here correctly.
04:54
1 minus 0 .11, which is 0 .17 .8.
04:58
Let them see here what we want to compute is what is the probability that given here that she will, she did not receive any mail on monday and tuesday and wednesday.
05:13
So let's write this as ntw complement.
05:18
She will be accepted if she do not get any mail until wednesday.
05:25
So here using the conditional probability, this is the same as if you open this.
05:30
Is this the probability of being accepted, which i'm going to write as a, so we'll better to simplify, and she do not receive any mail on these three days.
05:43
Then we need to divide this by the probability of not receiving any mail on these three days.
05:51
So basically, this probability that we have here at the beginning is the same as the probability of being accepted, times the probability of not receiving any mail on these three days, given that she was accepted, divided by the probability of not receiving any mail.
06:13
So let me put here tuesday until wednesday.
06:19
So this one here, because we have the complement, is the same as if you open this, one minus the probability of, in this case, the union.
06:29
So she did not receive, she received some kind of mail on monday or tuesday or wednesday.
06:37
At least one of these days, she received like a mail, given that she was accepted.
06:42
And then again, the probability that we have here, mtw complement.
06:48
No mail until wednesday.
06:50
So now, because like this one here means that basically she will receive like a mail in one of these days, not all of them.
07:00
So basically we can open this as the sum of these probabilities if she got like a mail on monday, given that she was accepted, plus the probability of getting only the mail on tuesday, given that she was accepted, or getting a mail here on wednesday, given that she was accepted.
07:21
And again, divided by this probability of this not receiving any mail until wednesday.
07:28
So here the probability of being accepted 0 .6, 1 minus...