But it is not fortuitous.
When writing copy, be careful with the words fortuitous and fortunate.
Fortuitous events happen by chance, randomly. While they need not be fortunate events, they often are, e.g., “It was purely fortuitous that the meter reader came along less than a minute after I returned to my car.”
Although fortunate events may be fortuitous, they might not be, e.g., “I was fortunate to return to my car just before the meter reader came around on his top-of-the-hour pass.”
When you mean random and unlucky, write random or one of its synonyms – accidental, haphazard, arbitrary, unplanned, unintentional. When you mean random and lucky, write fortuitous. When you mean lucky, write fortunate. Better yet, just use plain ol’ lucky to be sure everyone knows what you mean.
Adapted from “Common Errors in English Usage,” by Paul Brians.