by accident

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• adverb Accidentally; unintentionally; without meaning to; as the result of an event not expected, aided, or designed by one's will.
• adverb As the result of some undesigned, unintended, unrelated, natural, or random occurrence; as the unexpected and unforeseen result of formerly unrelated factors.
• adverb By chance; unexpectedly; as the result of an unrelated series of events.
• adjective Accidental; as the result of some unforeseen happening or series of events; unexpected; resulting from an event without the foresight, expectation, aid, or design of the person by whose agency it was caused; unintentional.