Your paraphrasing makes it a lot harder to understand the problem.

During a fixed period of time, the expected total sales for two different products is 3 items. The probability that product A has the most sales is 30%, that product B has the most sales is 15%, and that there are as many sales of product A as B is 25%.

No more than 8 could be sold? How is that? I don't see how you could use Poisson if you have a cap of 8. Poisson distributions have infinitely many outcomes. Are there just 4 of each product? You could try to apply Poisson, but there will be non-zero probability of selling more than 8 items.

Are you sure you didn't mean some other distribution?