laws of probability Suppose that there is a $60\%$ probability that the product will be a success on the market (that means, the probability of failure is $40\%$). If the product is a success, you will get a profit of $\$200,000$, and if it is a failure, you will incur a loss of $\$100,000$. Should you develop this product? How do you make a decision in this situation? Also, how can one come up with the probability of success (or failure)?

There really is no right or wrong answer to whether or not you should develop the product. We can at least come up with the expected profit (with the convention that a loss is negative profit). This is just:

$$\mathbb{E}(P)=\$200,000\times60\%+(-\$100,000\times40\%)=\$80,000$$

Since this is positive it might be decided to develop the product.

To come up with success and failure probabilities you would really need to define what you mean by "success" and "failure". It could be defined in terms of total number of units sold or perhaps total generated revenue or perhaps something else quantifiable and essential to the company's bottom line. Failure would then be defined as the complementary event or the even where say a minimum number of units is **NOT** sold or if you **fall short** of a certain revenue threshold. Again, the risk factors impacting "success" here are fairly open ended and depend on the uniqueness of the product.