Geometric Counting and Probability
When dealing with a probability problem involving discrete quantities, we often times just use the fact that probability is the ratio of the number of successful outcomes to the number of total outcomes.
However, we can have a situation where the quantities are continuous. We can still use the same notion that probability is the ratio of successful outcomes to total outcomes, but we cannot simply count the number of successful outcomes and the number of total outcomes. Instead, we have to find the size of each set. This is where we turn to geometric probability. We can usually translate a probability problem into a geometry problem. We can use length for one dimension, area for two dimensions, or volume for three dimensions.