All of the plausible Republican hopefuls have major flips on their resumes.
In that last quote, she is pretty clearly envisioning the event as plausible and feeling horribly for her brother.
Finally, the president became convinced there was no plausible alternative.
1540s, "acceptable, agreeable," from Latin plausibilis "deserving applause, acceptable," from plaus-, past participle stem of plaudere "to applaud" (see plaudit). Meaning "having the appearance of truth" is recorded from 1560s. Related: Plausibly.