fortuitously

This term describes events that occur by chance, but it carries a strong connotation of positive outcome. While it can technically mean "accidentally," it is almost exclusively used in contexts where the accident is beneficial or lucky. Using it for a negative accident would be pragmatically jarring and unnatural.

In terms of register, it is a formal word. In casual conversation, speakers typically replace it with "luckily" or "by chance." It is most appropriate for written reports, formal narratives, or professional correspondence where a more sophisticated tone is required to describe a serendipitous event.