Final answer:
The game designed by Shigeru Miyamoto where Mario originated is Donkey Kong. This 1981 arcade game marked the first appearance of Mario, then known as Jumpman, marking an important milestone in video gaming history.
Step-by-step explanation:
The game that Shigeru Miyamoto did much of the design for while in a Nintendo company bathtub, which is also the origin of Mario, is Donkey Kong. Shigeru Miyamoto is a famous game designer and producer who has worked on many popular Nintendo games. Donkey Kong was a pioneering arcade game released in 1981 and it was the first appearance of what would become the iconic character, Mario, although he was originally referred to as Jumpman. Mario subsequently became Nintendo's mascot and starred in his own series starting with Super Mario Bros., but it was indeed Donkey Kong where he made his debut.