I was recently asked why Voiculescu developed free probability theory. I am not very expert in this and the only answer I was able to provide is the classical one: he was challenging the isomorphism problem of whether $II_1$-factors associated to two different free groups are isomorphic or not. First: is this true or just legend? Were there any other motivations? In particular I would be interested in more down-to-earth motivations, something that could theoretically be explained to someone with basic knowledge in probability theory and operator theory (without necessarily knowing what a $II_1$-factor is).
Thanks in advance!