Suppose I want to write a software. I know that:
- The probability I can overcome the technical difficulties is $p_1$
- The probability I can do all the work before I get too tired to complete it is $p_2$
- The probability I can get to sell it with profit $x$ is $p_3$
Assuming all events are independent, what would be my profit? Better yet could function be derived that would describe the profit value based on $p_1, p_2, p_3$.
Could I assume that $$ProbabiltyOfProfit_x(p_1, p_2, p_3)=p_1p_2p_3$$
One problem with this formula is that if I could not build the product, this is a probability of value $(1-p1*p2)$, then selling the product will not be logically possible.
Product selling, with probability $p3$ requires a product to exist in the first place. Accordingly I am not sure that $p3$ is independent of $p1,p2$.
How could this function be better formulated if correct?
Note: This is not homework.