# How do you calculate the probability associated with each possible sum of the numbers expressible by the roll of a set of weighted dice?

Suppose you want to plot the probability distribution that you will make money manufacturing widgets. You have a table of the probabilities associated with the various prices you might be able to negotiate from a widget-component supplier; you have a table of the probabilities associated with the costs of assembling the widgets; and you have a table of the probability of the prices that you might be able to sell the widgets for.

I presume one way to do it would be to proceed by brute force and multiply the probabilities for each possible combination. Is there a more efficient way to compute the answers?

Practically speaking, is there a way this can be done more efficiently using a spreadsheet program?

You are describing three random variables ($$C_{supplier}$$, $$C_{assembly}$$, $$P$$), and a fourth one that is profit $$\pi = P - C_{supplier} - C_{assembly}$$.
If you can reasonably approximate all of these variables with Normal distributions, and reasonably assume they are independent, then a reasonable estimate of the mean (variance) of profit is the mean (variance) of $$P$$ minus the means (variances) of $$C_{supplier}$$ and $$C_{assembly}$$: