Law of Total Expectation

The Law of Total Expectation states that the overall average outcome of a situation can be found by considering all possible scenarios and their probabilities. In other words, if you break down a complex event into smaller, simpler parts, you can find the overall expected value by averaging the expected outcomes of each part, weighted by how likely each part is to occur. This helps manage uncertainty by combining different possible situations into a single, comprehensive average, making it easier to understand or predict what to expect on average.