Mathematics
The Law of Total Probability and Partitioning Events
Quick fact
The law of total probability lets you find the probability of an event by averaging its conditional probabilities over a partition of the sample space, weighted by the probabilities of the partition parts. For example, the overall probability of a positive test result is the sum of true positive and false positive rates, weighted by how common the condition is.
Why this is interesting
You know the probability it rains on a random day, but have you ever wondered how to compute it when you only know the chances of rain given the season? The law of total probability is the key.