They met by accident. [=by chance]他们碰巧遇上了。

She says that she became pregnant by accident. [=unintentionally]她说她意外怀孕了。

Scientists discovered the vaccine almost/quite/entirely by accident.科学家们发现这种疫苗，几乎/实在/完全是个偶然。

Did it happen by accident [=accidentally] or by design?这件事是意外还是事先设计好的？