Let's say I have a situation where I spend X dollars on a product that contains a set of items that go for specific individual retail prices and I know the probabilities of getting each item in the set of products I buy. Is there a way to tell if my return Y will be greater than X over the long run?
For example, say I am given a list of N (say, N=100) items along with their probabilities and individual retail prices that I buy in a set of M items, where M < N (for example, M=10), for X dollars (let's assume 10). Is there a formula I can plug these values into in order to determine if I will make profit over the long term of buying these items in random lots and selling these items individually?
I know it's easy to tell that you will make profit if all the items are worth more than \1, and that it is easy to show that you will lose profit if all the items are worth less than \$1 individually. But how can you tell if the values and probabilities of all these items vary?