This seems more accurate and realistic about the source of the discrepancy:
Rich people have the luxury to choose which risks they take and make calculated endeavors, but are never forced to take a risk and have great ability to manage their total exposure to risk.
Poor people are inundated with being forced to take bad risks and manage the danger between them constantly, such that they can't properly gather resources to take on additional voluntary risks (even when they have an expected reward) because it poses too much systemic danger with the additional risk.
That said, once you count in drug sales, the poorest 10% of people I know have a higher per capita entrepreneurship rate than the richest 10%. So in practice, poor people are actually taking on business risk at a higher rate as well, though it's again motivated by necessity.
The biggest discrepancy is, of course, access to capital and explain the vast majority of the discrepancy in outcome.