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. (Enter your answers in set notation. Enter EMPTY or ∅ for the empty set.)
(a) List the outcomes in .
 = 
  
Incorrect: Your answer is incorrect.


(b) Let A denote the event that exactly one book must be examined. What outcomes are in A?
A = 
  
Correct: Your answer is correct.


(c) Let B be the event that book 5 is the one selected. What outcomes are in B?
B = 
  
Incorrect: Your answer is incorrect.


(d) Let C be the event that book 1 is not examined. What outcomes are in C?
C = 
  
Correct: Your answer is correct.

Let's address the parts of the problem one by one.

### Part (a)
**Question**: List the outcomes for the scenario where a student examines the books in random order and stops when a second printing has been selected.

- There are 2 first printings (books 1 and 2) and 3 second printings (books 3, 4, and 5).
- The student stops when a second printing is selected, so each outcome must end with either book 3, 4, or 5.
- The order of examination matters because the student randomly examines books, and stops after the first second printing.

Thus, the possible outcomes are as follows:
- The student examines one book and it's a second printing. These outcomes are: {3}, {4}, {5}.
- The student examines one or more first printings before selecting a second printing. These outcomes are: {13}, {14}, {15}, {23}, {24}, {25}, {213}, {214}, {215}.

So, the complete list of outcomes in set notation is:
\[
\{3, 4, 5, 13, 14, 15, 23, 24, 25, 213, 214, 215\}
\]

### Part (b)
**Question**: Let \( A \) denote the event that exactly one book must be examined. What outcomes are in \( A \)?

- For exactly one book to be examined, the first book must be a second printing (since the student stops after selecting a second printing).
  
Thus, the outcomes in \( A \) are:
\[
A = \{3, 4, 5\}
\]

### Part (c)
**Question**: Let \( B \) be the event that book 5 is the one selected. What outcomes are in \( B \)?

- Book 5 is selected, and the student stops as soon as they encounter book 5.
- This means that book 5 must be the last book in the sequence.

The outcomes where book 5 is the last book examined are:
\[
B = \{5, 15, 25, 215\}
\]

### Part (d)
**Question**: Let \( C \) be the event that book 1 is not examined. What outcomes are in \( C \)?

- In this event, book 1 cannot appear in the sequence.

The outcomes that do not contain book 1 are:
\[
C = \{3, 4, 5, 23, 24, 25\}
\]

Let me know if you want any more details or have any questions. Here are five related questions:

1. What is the probability of selecting a first printing in the first round?
2. How many different outcomes are possible if the student examines all five books?
3. What is the likelihood of examining exactly two books before selecting a second printing?
4. Can this scenario be modeled using a geometric distribution? If so, how?
5. How would the outcomes change if there were more than two types of printings?

**Tip**: When working with random selection problems, clearly define your stopping condition to determine the valid outcomes.

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. (Enter your answers in set notation. Enter EMPTY or ∅ for the empty set.) (a) List the outcomes in set notation. (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?

Solve a combinatorics and set theory problem involving five copies of a text on reserve. Learn how to list outcomes, define events, and calculate probabilities. This detailed guide is suitable for Grades 11-12, covering key concepts in set notation and event probability.

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