Which cloud deployment model is MOST likely to offer free or very cheap services to...

Public clouds offer services to anyone, regardless of affiliation, and are the most likely to offer free services to users. Examples of public clouds with free services include iCloud, Dropbox, and OneDrive. Private cloud models are designed for specific customers and for their needs, and would not offer services to the public at large, for free or otherwise. A community cloud is specific to a group of similar organizations and would not offer free or widely available public services. A hybrid cloud model would not fit the specifics of the question.