I often hear complaints from movie-goers who think that the trailers run before the movies they bought tickets to see are inappropriate. This has become even more important now that the MPAA has made the rules about content in trailers even more opaque, Slate explains how trailers are assigned to films. For the chains, it works according to

The “quadrant” system. As many as six trailers play before features at major chains, like AMC and Regal. The studio releasing a given film typically has automatic rights to two of these slots, and theater executives (in consultation with higher-ups from various studios) select the remaining four. Though theoretically studios and theaters could attach any trailer to any movie, they usually decide which releases to promote by using the “quadrant” system, which divides potential audiences into four different categories: men under 25, women under 25, men over 25, and women over 25.

This does not apply to independent theaters, which select trailers for films they will be showing.