'haphazardly-disposed' is a Modern English compound formed from 'haphazardly' and 'disposed'. 'Haphazardly' derives from 'haphazard' + the adverbial suffix '-ly'; 'haphazard' itself is an English blend of 'hap' (chance) and 'hazard'. 'Disposed' comes from the verb 'dispose' (see below).

'haphazard' appeared in Early Modern English (16th century) as a combination of 'hap' (Old Norse/Old English for 'chance') and 'hazard' (from Old French 'hasard', ultimately from Arabic 'az-zahr' meaning 'dice'). 'Haphazard' later took the adverbial form 'haphazardly'. 'Dispose' comes from Latin 'disponere' (dis- 'apart' + ponere 'to place'), through Old French/Middle English into modern English; 'disposed' is the past participle used adjectivally.

Initially, elements meant 'chance' ('hap') and 'risk/dice' ('hazard'), so 'haphazard' originally conveyed 'by chance or risk'; over time 'haphazard' and 'haphazardly' generalized to mean 'random, careless, or unplanned'. 'Dispose' originally meant 'to place or arrange' (from Latin), and 'disposed' came to be used as an adjective meaning 'placed' or 'disposed (of)'; combined, the compound now means 'placed or discarded in a random/careless way.'