The problem asks for the probability that the next movie shown at the Cinemania theater is an action movie, given that the theater showed 108 movies last year, and 15 of them were action movies.

1. Problem Description

The problem asks for the probability that the next movie shown at the Cinemania theater is an action movie, given that the theater showed 108 movies last year, and 15 of them were action movies.

2. Solution Steps

The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the favorable outcome is that the movie is an action movie, and the total number of possible outcomes is the total number of movies shown.

The number of action movies is

1

5. The total number of movies is

1

0

8. Therefore, the probability that the next movie is an action movie is $\frac{15}{108}$.

3. Final Answer

$\frac{15}{108}$