Geometry

Question Analysis
This question involves calculating the probability of mutually exclusive events within the context of a library book selection.
The main focus is on recognizing that a book cannot be both fiction only and non - fiction only at the same time, making these two events mutually exclusive, and applying the addition rule for mutually exclusive events, , to find the probability of a randomly selected book being either fiction or non - fiction.

Key Concept Explanation
Mutually exclusive events, in this case, mean that the categories of fiction only and non - fiction only do not overlap.
For mutually exclusive events (selecting a fiction - only book) and (selecting a non - fiction - only book), the probability of either event occurring is the sum of their individual probabilities because .

Step - by - Step Solution
First, identify the number of favorable outcomes for each event and the total number of outcomes.
The total number of books in the library is 150, which is the total number of possible outcomes when selecting a book.
Calculate the probability of event (selecting a fiction - only book).
There are 45 fiction - only books, so .
Calculate the probability of event (selecting a non - fiction - only book).
There are 35 non - fiction - only books, so

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