Questions: A shelf holds 12 books. Eight are fiction and the rest are nonfiction. Each is a different book with a unique title. The fiction books are numbered one to eight. The nonfiction books are numbered one to four. Randomly select one book Let F= event that book is fiction Let N= event that book is nonfiction What is the sample space?

Solution Steps

To determine the sample space, we need to list all possible outcomes of selecting one book from the shelf. Since there are 12 books in total, each with a unique title, the sample space will consist of all these individual books.

The shelf holds a total of 12 books, consisting of 8 fiction books and 4 nonfiction books. Each book is unique and can be identified by its title.

The sample space \( S \) is the set of all possible outcomes when selecting one book from the shelf. Since each book is unique, the sample space consists of all 12 books.

The sample space can be explicitly listed as follows: \[ S = \{\text{Fiction 1}, \text{Fiction 2}, \text{Fiction 3}, \text{Fiction 4}, \text{Fiction 5}, \text{Fiction 6}, \text{Fiction 7}, \text{Fiction 8}, \text{Nonfiction 1}, \text{Nonfiction 2}, \text{Nonfiction 3}, \text{Nonfiction 4}\} \]

Final Answer