By Chance, Unexpectedly, Coincidence
adverb, noun, な adjective, の adjective
Accidentally but naturally (as in nothing was set up artificially before). So the accident was a true, natural accident. This kind of accident is something that happens by chance, or unexpectedly. In other words, a coincidence.
ぐうぜん
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
偶然の一致に思わず笑ってしまった。
I couldn't help but laugh at the coincidence.
偶然なショットだけど、いい写真が撮れた。
It was an accidental shot, but it turned out to be a good photo.
空港で偶然、高校時代の友人に会ったんですよ。
I unexpectedly ran into a friend from high school at the airport.