Probability
The Birthday paradox only seems like a paradox because it unexpectedly challenges our perception of probability. It states that in a group of only 23 individuals, there is more than a 50% chance that at least two are sharing a birthday. Although it may seem counterintuitive, we have the math that proves and supports this statement.
In this article, we will gradually reprogram our intuition and build the knowledge required to derive the expression that proves the paradox. This blog focuses on software engineering and system design so we will follow a real-world example of this problem found in software. But first, let’s start with basic counting.
Probabilistic functions can model many algorithms and procedures. They can help us optimize procedures to produce the best results. Experienced software engineers know that at some point, almost any software will reach some level of non-determinism, where a solution is not absolute but approaches the best results if using the optimal configuration. Mathematically, such a solution usually boils down to finding minima, maxima or limits of some probabilistic functions.
In this article, we will explore the beautiful math behind Bloom filters. We will explore the accuracy and trade-offs of Bloom filters and see why a Bloom filter can be an excellent choice for some cases, especially in Big Data, OLAP systems, dealing with huge and fairly static datasets.
