"not having an appearance of truth or credibility," 1670s, from assimilated form of in- "not, opposite of" (see in- (1)) + plausible. Earlier it meant "not worthy of applause" (c. 1600). Related: Implausibly.
word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
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."