How is 'fortuitously' best defined in the context provided?

The word "fortuitously" is best defined as occurring by accident or chance, particularly in a favorable manner. This definition points to an event or situation that happens unexpectedly, yet it turns out to have a beneficial outcome.

In context, if something transpires fortuitously, it suggests that while there was no explicit planning or intention for such an occurrence, it happened serendipitously and resulted in a positive effect. This aligns well with situations in life where unexpected opportunities arise, leading to advantageous results that one could not have predicted.

The other definitions do not fit this context; they imply elements of planning or risk-taking that do not correspond to the essence of fortuitous occurrences. By focusing on serendipity and the favorable nature of the event, the selected definition captures the intended meaning perfectly.