The Cinemania theater showed 108 different movies last year. Of those, 15 movies were action movies. We need to find a reasonable estimate of the probability that the next movie is an action movie.

1. Problem Description

The Cinemania theater showed 108 different movies last year. Of those, 15 movies were action movies. We need to find a reasonable estimate of the probability that the next movie is an action movie.

2. Solution Steps

The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcome is that the next 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. So the probability that the next movie is an action movie is the number of action movies divided by the total number of movies, which is $\frac{15}{108}$.

3. Final Answer

$\frac{15}{108}$