Disclaimer: I am not a mathematician!
I have encountered a problem at work. There are a number of products $P$, a number of stores at a large retailer (branches, $B$) and a number of days ($D$). I need to calculate the probability that a product $p$ will sell ($S$) on a particular day $d$ at a particular branch $b$.
I know the probability that a given product will sell on a given day: $\mathbb{P}(S\mid D=d, P=p).$ I also know the probability that a branch makes a sale on a given day: $\mathbb{P}(S\mid D=d, B=b).$
How do I calculate the probability of a sale of a product at a branch on a day? i.e. from the given information, how do I get the distribution $\mathbb{P}(S\mid D=d, P=p, B=b)$?
Thank you for your help!