1Something that happens by chance rather than by design; a coincidence or accident.
これはただの偶然だと思う。
I think this is just a coincidence.
二人が同じ夢を見たのは偶然の一致だった。
It was a coincidence that the two of them had the same dream.
その事故は偶然が重なって起きた。
That accident happened because a series of coincidences overlapped.
2By chance; unexpectedly—used adverbially to describe something happening without prior intent.
駅で偶然、昔の同僚に会った。
I ran into a former coworker by chance at the station.
その本を偶然見つけて、思わず買ってしまった。
I happened to find that book and ended up buying it on impulse.
偶然にも、二人は同じ日に生まれていた。
By coincidence, the two of them were born on the same day.
3In philosophy, contingency—the state of something that could have been otherwise, as opposed to necessity.
その哲学者は偶然と必然の関係について論じた。
That philosopher discussed the relationship between contingency and necessity.