fortuitous
Meaning: happening by chance, often lucky or fortunate
Usage: After looking for Manuel and not finding him at home, Harriet had a fortuitous encounter with him at the post office.
serendipity
Meaning: luck, finding good things without looking for them
Usage: In an amazing bit of serendipity, penniless Paula found a $20 bill in the subway station.
hapless
Meaning: unlucky
Usage: My poor, hapless family never seems to pick a sunny week to go on vacation.
vicissitude
Meaning: a change in circumstances, often difficult or unexpected
Usage: The vicissitudes of daily life prevent me from predicting what might happen from one day to the next.
arbitrary
Meaning: based on factors that appear random
Usage: The boy’s decision to choose one college over another seems arbitrary.