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SIG Quantitative Trader Interview Question: Card Probability Problems from a Standard Deck

Quantitative trading interviews at leading firms like SIG (Susquehanna International Group) often feature probability problems based on standard decks of cards. These questions assess a candidate’s mathematical reasoning, combinatorial skills, and ability to communicate complex solutions clearly. One classic interview scenario involves calculating the probability of drawing a specific number of aces or other cards in a subset of draws from a standard 52-card deck. This article provides a comprehensive, step-by-step guide to solving such card probability problems, focusing on both the underlying concepts and the detailed calculation methods you’ll need to ace your SIG Quantitative Trader interview.

Card probability questions are a staple in quantitative trading interviews because they test your grasp of combinatorics, probability theory, and logical reasoning. These problems often take the form:

Before delving into specific problems and solutions, let’s clarify the foundational concepts that underpin these calculations.