Final answer:
To find the number of non-mystery books, subtract the number of mystery books from the total number of books, yielding 87 non-mystery books. Moreover, the sum of the probabilities of an event and its complement is always 1.
Step-by-step explanation:
To find the number of outcomes in the complement of the given event, which in this case is selecting a book that isn't a mystery from a bookcase of 266 books wherein 179 are mysteries, we need to subtract the number of mystery books from the total number of books. The complement here refers to the event of selecting a book that is not a mystery. So, we simply perform the subtraction:
Total number of books - Number of mystery books = Number of non-mystery books
266 - 179 = 87
Therefore, there are 87 outcomes in the complement of the given event, where the event is selecting a mystery book from the bookcase.
The sum of the probabilities of an event and its complement is always 1 since an event and its complement together comprise all possible outcomes. This can be represented as:
P(Event) + P(Complement of Event) = 1