'randomly-determined' originates from the combination of 'randomly' and 'determined', where 'randomly' comes from 'random', meaning 'without a definite aim, direction, rule, or method', and 'determined' from 'determine', meaning 'to decide or conclude'.

'randomly' evolved from the Middle English 'randoun', and 'determined' from the Old French 'determiner', eventually forming the modern English term 'randomly-determined'.

Initially, 'randomly' meant 'without a fixed course', and 'determined' meant 'decided'. Together, they evolved to mean 'decided by chance'.