It is my understanding that the Poisson Theory applies in the following question but I still require help -

Given a fixed period of time what is the probablity of any number of sales for each product given that the expected total sales on average is 3.

Product A most sales 60%

Product B most sales 15%

Equal Sales 25%

Expected sales

3

Knowing these values, what is the probability of

Product A 0 sales & Product B 0 sales

Product A 1 sale & Product B 1 sale

Product A 1 sale & Product B 0 sales

Product A 3 sales & Product B 1 sale

and so on etc

When all variations of sales (with the most that could possibly be sold is 8) are calculated they should equal the corresponding expected sales i.e 0-0, 1-1, 2-2. 3-3, 4-4 should be the same as Equal Sales of 25% and the same for the others.

I hope i have explained the problem well enough and would appreciate any helpful comments or answers.

I have been using excel to calcuate this but there appear to be a number of inconsistancies when any of the starting values are changed.