Expected Values: Cutting down on computational costs of the European binomial options pricing model

This paper explains more probability theory and goes into the concept of expected values on finitie probability spaces. It goes into conditional expectations of a coin toss as a primer. Then it explains how expected values underly the binomial options pricing formual. It then demonstrates how this knowledge can be used to abreviated the binomial options pricing model for European options. This abreviation both goes to demonstrate the core concept and serves as means to cut down on computational costs.