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TL;DR

Bloom Filter False Positive Rate: A canonical quantitative trading interview question at intermediate difficulty. Commonly asked at Two Sigma, Citadel, DE Shaw.

By Valenke Exam Prep Team·Last updated 2026-06-01
intermediateRandomized Data Structures

Bloom Filter False Positive Rate

Asked at: Two Sigma, Citadel, DE Shaw

Problem
A Bloom filter uses mm bits and kk independent hash functions. After inserting nn elements, derive the false positive probability. What is the optimal number of hash functions kk^* that minimizes this probability?

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