Question

A library has five copies of a certain textbook on reserve of which 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. a. Display the possible outcomes in a tree diagram. b. What outcomes are contained in the event \(A\), that exactly one book is examined before the chance experiment terminates? c. What outcomes are contained in the event \(C\), that the chance experiment terminates with the examination of book \(5 ?\)

Short answer

Event A contains outcomes where books 3, 4 or 5 are picked first. Event C will contain outcomes where book 5 is picked first, or one of books 1 or 2 is picked followed by book 5.

Step-by-step solution

- Generating the Tree Diagram

All possible outcomes can be displayed in a tree diagram. Starting from the left, each branch would represent a pick. Branches would end whenever a second printing book is picked. Follow this method until all possible combinations of selections have been represented.

- Determine outcomes for event A

Event A requires only one book to be examined before the experiment terminates, i.e., the first book picked is a second printing. Therefore, the outcomes in Event A would be the selections where any of the second printing books (3,4,5) are picked in the first attempt.

- Determine outcomes for event C

Event C requires that the experiment ends when book 5, a second printing, is picked. Therefore, to get the outcomes for event C, consider each path on the tree diagram where the last book picked is book 5. Remember that the experiment stops as soon as a second printing book is chosen.