00:01
So we're given a scenario where we have five total pens in a container on our desk.
00:09
Three will write and two are defective.
00:20
All right.
00:21
And we're going to ask some questions about this.
00:23
Oh, and also, before we get to our questions, we're going to say that we are going to randomly select two pens without replacement.
00:48
And then given this scenario, we're going to answer some questions.
00:51
The first question, we're going to let x be the number of defective pens.
01:05
I'll spell that wrong.
01:07
Defective.
01:16
X is a defective pens.
01:18
And x is a random variable.
01:21
And this is going to be a hyper geometric distribution.
01:35
Now, it was a drop -down item, a drop -down menu.
01:40
We're not only told what the items were, but with the selection items were, but it's a hypergeometric distribution.
01:48
You know, like i said, we're not really sure what the drop -time mean were, but what type of distribution it would be.
01:55
And the next question says, for each pen chose from the container, we consider defective as a success and working as a failure, since we're interested in both pens being defective.
02:07
So this would be true.
02:08
So we're going to define a success, and we often just put this in quotes.
02:17
Quote, success is equal to the defective because we're looking for the number of defectives, the number of defective pens.
02:31
So that means it's like success.
02:33
So the probability of a success means the probability of a being.
02:37
And then working would be, then a failure would be award.
02:45
Working pen because it works.
02:48
It works, but you care about the number of defectives.
02:53
All right.
02:54
Now, question c, this is a true false statement.
02:58
This, based on this, x is a well approximated by a binomial distribution.
03:05
We'll be it with binome with n equals two, and p .i, the probability is equal to two -fifths.
03:15
And this is false.
03:16
And the reason it's false is because a binomial distribution assumes that this probability is constant for each selection.
03:24
And it's not because we are selecting the pens without replacement.
03:31
So sure, at the beginning there are five defectives, or five pens, two of which are defective, and then you've got working, working, working, right? but let's just say you grab a defective, you hit one of those two fifths...