Avg Tosses for 3 Heads in a Row
Average tosses for three heads row is a medium quant interview question on Expected Value, reported to have been seen at Citadel, Goldman Sachs, IMC, Jane Street, Squarepoint Capital, Two Sigma and WorldQuant.
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This classic quant interview question is about expectation in stochastic processes and patterns in repeated independent trials. It sits at the intersection of probability theory and discrete-time Markov dynamics, a core topic in quantitative finance interviews. Candidates on MyQuantPartner will recognize it as a gateway problem linking simple coin tosses to more complex sequence-detection models used in trading and risk.
It trains your ability to decompose a random process into states that summarize all relevant information, then express the expected remaining time to a target pattern from each state. You practice setting up interdependent expectations, recognizing how progress toward the goal can be lost, and keeping track of how randomness affects future waiting times. This is central to strong quant prep.
It matters for quant interviews because it mirrors how quants think about time to events: default, barrier hits, signal confirmation, or execution conditions. Interviewers use it to see if you can translate a verbal description of a random mechanism into a rigorous state-based expectation framework. Being fluent with such problems shows you can handle Markov models, hitting times, and structured probabilistic reasoning, all of which are heavily used in pricing, risk, and algorithmic trading.
What it tests
Problems that ask for the expected number of steps to reach a specific sequence in a random process are governed by the principle of Markov chains and state-based recursion. The process can be modeled as a set of states, each representing the current progress toward the desired sequence (such as the number of consecutive heads). The expected value from each state depends only on the current state, not the history, because of the memoryless property of independent trials. By setting up equations for the expected number of steps from each state, and expressing each in terms of the others, you can solve a system of linear equations to find the answer. This structure holds because the process always either advances toward the goal or resets, and each transition's probability is fixed by the rules of the random process.
Practise this question with written feedback, or hear it in a spoken mock interview.
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