Final answer:
The true ratio of non-fiction to fiction books on the shelf is 4:8, simplified to 1:2, but none of the multiple-choice answers match this ratio. In probability, the sum of the probabilities of an event and its complement is always equal to 1.
Step-by-step explanation:
The question provided relates to the ratio of non-fiction to fiction books in the school library. Given a shelf that holds 12 books with 8 fiction and 4 nonfiction books, we can determine the ratio by comparing the quantities of each type. Since there are 8 fiction and 4 nonfiction books, the ratio of non-fiction to fiction books is 4:8.
This simplifies to 1:2, which would be half as many non-fiction books to fiction books. However, this option isn't presented in the possible answers. If the student is asking within the context of these specific available answers, there appears to be a discrepancy as the correct ratio isn't listed. Thus, it is important to clarify the question or the given information.
In probability theory, the sum of the probabilities of an event and its complement is always 1. The complement of an event is the set of all outcomes in the sample space that are not part of the event itself. For instance, in the example of selecting books from the shelf, if the event F represents selecting a fiction book, then its complement would be selecting a non-fiction book, or event N. T
he probability of selecting a fiction book (F) plus the probability of selecting a non-fiction book (N) equals 1, which means 100% certainty that either a fiction or nonfiction book will be chosen.