1540s, "acceptable, agreeable; deserving applause or approval" (senses now obsolete), from Latin plausibilis "praiseworthy, pleasing, acceptable," from plaus-, past-participle stem of plaudere "to applaud" (see plaudit). Meaning "having the appearance of truth, apparently right, seemingly worthy of acceptance or approval" is recorded from 1560s; especially "having a specious or superficial appearance of trustworthiness." Related: Plausibly.
The expression plausible deniability emerged during the Watergate scandal (1973) but is said to be from CIA jargon in the 1950s (Allen Dulles sometimes is credited with the first public use); the thing itself is older: "the situation that allows senior officials or powers to deny responsibility for discreditable actions by others in their hierarchy because no one can confirm the deniers knew of the actions."
word-forming element making abstract nouns from adjectives and meaning "condition or quality of being ______," from Middle English -ite, from Old French -ete (Modern French -ité) and directly from Latin -itatem (nominative -itas), suffix denoting state or condition, composed of -i- (from the stem or else a connective) + the common abstract suffix -tas (see -ty (2)).
Roughly, the word in -ity usually means the quality of being what the adjective describes, or concretely an instance of the quality, or collectively all the instances; & the word in -ism means the disposition, or collectively all those who feel it. [Fowler]
<a href="https://www.etymonline.com/word/plausibility">Etymology of plausibility by etymonline</a>
Harper, D. (n.d.). Etymology of plausibility. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/plausibility