Which of the following is an individual event designed to show the athletic ability of a ranch type horse in the confines of a show arena?

Jumping is generally not characterized as an individual event designed specifically to showcase the athletic ability of a ranch-type horse in a show arena. Instead, reining would be the correct choice for the type of event mentioned in the question.

Reining includes a variety of maneuvers that demonstrate the horse's agility, speed, and ability to perform specific tasks that are reflective of ranch work. Collaborative horse-rider performance is central to reining, showcasing skills in stopping, spinning, and galloping in smooth patterns. This event is particularly tailored to evaluate the agility and responsiveness of ranch-bred horses, making it well-suited for the defined context of the question.

Jumping, on the other hand, focuses on the horse's ability to clear obstacles and is typically more associated with performance events than specific ranch-type tasks. Dressage is an event centered on precision and training, primarily demonstrating the horse's ability to follow commands with grace. Halters are primarily used to evaluate the conformation and structure of the horse rather than its athletic performance in the arena.