Final answer:
When household computers were becoming common, the most likely operating system would have been MS-DOS or the early versions of Windows. MS-DOS was prevalent during the early to mid-1980s before graphical user interfaces popularized by Apple's Macintosh in 1984 led to the widespread adoption of Windows.
Step-by-step explanation:
The operating system most likely on Gracie's grandfather's household computer when these devices were becoming more common would have been either MS-DOS or Windows. During the early to mid-1980s, as computers proliferated in various spheres such as government offices, private firms, and family homes, MS-DOS was extensively used as the foundational operating system for IBM PCs. Notably, in 1984, Apple introduced the Macintosh, employing a graphical user interface, which set a new standard for user-friendliness in operating systems. Around this time, Microsoft and other companies would have started incorporating graphical user interfaces into their systems leading to the increasing popularity of Windows. However, in the beginning, when computers first became items for household use, MS-DOS was considerably more prevalent than the then-nascent Windows environment.
It's important to note that while other operating systems like UNIX and IBM's proprietary systems were in use, they were more common in institutional and specialized environments rather than in household personal computers during the early stages of their adoption by the general public.