Response to the following problem:
Suppose that an investment of 1 million dollars leads after 1 year, to a project worth 3 million dollars with probability 50% and to a complete loss of the million dollar investment the other half of the time. This is a high-risk, high-return project. Now, suppose that this project can be turned into 1000 smaller projects, each of which costs $1000 to begin and each of which returns either $3000 or $0 with equal probability.
Finally, suppose that the success of each of the small projects is independent of the success of the other projects show that investing in the 1000 smaller projects has the same return but a much reduced risk relative to investing in the single large project.