What does the phrase "by mistake" imply?

The phrase "by mistake" implies an action that is unintentional or accidental. When something happens "by mistake," it means that it was not done deliberately or with intention; rather, it occurred due to an oversight or error. This aligns perfectly with the choice that describes the occurrence as being accidental. For example, if someone sends an email to the wrong recipient "by mistake," it indicates that they did not plan to send it to that person; it was an unintentional act. The other options, which suggest deliberate action or focus, do not capture the essence of this phrase.