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# A college library has five copies of a certain text on reserve. Two copies $(1$ and 2$)$ are first printings, and the other three $(3,4,$ and 5$)$ are second printings. A student examines these books in random order, stopping only when a second printing has been selected. One possible outcome is $5,$ and another is $213 .$(a) List the outcomes in $\mathcal{S}$ .(b) Let $A$ denote the event that exactly one book must be examined. What outcomes are in $A ?$(c) Let $B$ be the event that book 5 is the one selected. What outcomes are in $B ?$(d) Let $C$ be the event that book 1 is not examined. What outcomes are in $C ?$

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#### Topics

Probability Topics

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### Video Transcript

right, Question eight, We have five copies of the text text one in text to our first prince, and then text 34 and five or second Prince. Um, what happens in this problem is that, um, student examines the texts, um, in order until one of them's a second, Actually, randomly starts like text examines them until he or she gets a second. All right, so let's do the the worst case scenarios first. Okay, So the shortest lists would be, um, three. So that would be. Got it on the first. Got a second print on the first try, and it was three. Another one would be five. Another one would be for Okay. So those air just one number lists the iceberg is out of a market three or we're back. Picked a second edition on the 1st 1 Didn't he? Melts. Okay, So the next thing to do is what, um, you were then done on a second tribe. Okay, so that would be, for instance, one, then three or one that for for one than five. That would be all times when the student would stop after two yeses. And then the other possibility would be gets a first. The other first copy then stops with three second copy starts with stuff war second, coffee starts stops when he gets a five. What? So these two have exhaust that any the next? After. That would be, uh what if, um, the longest string would be what the person examined but one book, too. Then stop three or book one and then read book to stop before it could be one, too. And then five, right? This first to you could have these could be switched the one and two. So you go to one three. And that would be different from the 123 meant to 14 and then 215 Okay, that'd be another example. Um uh, then you see, I believe that would be all of the possibility track. There won t 3456789 10 11 12 13 15 once. Yeah, right. Next. You don't have lots of parts to them. Let aid to note that the event that denote the event that exactly one book must be examined where the outcomes, uh, are in a so it only one book is examined. That means we're talking about this. This and this is the only ways they have one book, one book examined. All the rest of them have two more. All right, um hey, was this sample space? Okay, So, see, um, B is the event that Book five is the one selected. And then where the out What outcomes aren't be you. So, be is the event that Book five is the one select where the outcomes be, Um, so there would be only one possibility for that. Okay, that would be, um, this one I was selected. If I'm reading that the way that would think it said, that's what it would be for that, Um, this is the one selection selected. I'm not a one selected, um, or eight books. Okay, then. See, um is the event that one is not examined. Okay, so we're looking for all the possibilities where Book one is not examined. Book one one. Not Fred. We go through our list with four ones where Book one is not red. So that would be three red for red. I read throughout this throughout this. This there's no one you know, one one. That one. That one that one one guy. One guy. So it be this six, um, six albums once that are circled, right, right. Only.

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#### Topics

Probability Topics