There´s a link between homotopy algebra and probability theory connecting morphisms of homotopy algebras and cumulants in probability theory. Jae-Suk talked about a similar topic when he was at Penn in the Fall, my talk will be different---it will have a deformation theory framework and some examples--- and I won't be assuming anything either. I´ll explain the link to cumulants, then explain how to expand this link to develop a homotopy theory of probability that allows derived mathematics to play a role in probability theory.