Expected value is defined as a weighted average, so this covers your first example. I have trouble understanding your setup in the second example. How is your lacking $10 to survive is related to the 30% chance of saving 10 people?
Expected value is defined as a weighted average, so this covers your first example. I have trouble understanding your setup in the second example. How is your lacking $10 to survive is related to the 30% chance of saving 10 people?