Easy · Probability & Combinatorics · Numerical · ~4 min · #65

Will the Next Card Be Higher?

Real interview · Susquehanna (SIG)

From a shuffled 52-card deck you turn over the top card, then the next. What is the probability that the second card has a strictly higher rank than the first (aces high, suits ignored)?

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Worked solution

Give the problem an honest attempt first, then reveal the full explanation.

Reported in interviews

Susquehanna (SIG)Glassdoor interview question
Asked as a betting question with follow-ups on bet sizing.

Candidate-reported and unverified; the firm may phrase it differently or no longer ask it. The wording here is our own paraphrase, and the solution was written and checked independently of any answers posted at the source.

Concepts

SymmetryComplementary counting

Relevant for

Quant TraderDesk Quant