The definition of independence of two events in a sample space is that the probability of the one doesn't depend on the other: $$ P(A|B) = P(A) $$ This definition feels necessary, but not sufficient. I can imagine at least two complicating cases:
I'm watching "Mugsy Explains" on "How flowering plants conquered the Earth".
One of the things this presenter does is to blur the distinction between "haploid organism" versus "diploid organism," instead of talking about whether more of the organism's life cycle is spent in a haploid phase versus a diploid phase.