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Sample Question of the Week

Can you solve this classic probability question from Jane Street?

MediumProbability

The HHT vs HTH Coin Flip

You flip a fair coin repeatedly. You want to see the sequence Heads-Heads-Tails (HHT). Your opponent wants to see Heads-Tails-Heads (HTH). Who is more likely to win, and what is the probability?

Show Solution

Answer: HHT wins with probability 2/3.

Let's analyze the winning conditions. For HTH to appear, you need the sequence HT. However, if HH appears first, you are now waiting for T to complete HHT. Once HH appears, it is impossible for HTH to appear before HHT, because HTH requires a T after the first H, but we already have HH.

The only way HTH wins is if the sequence starts with HT... and eventually hits H without seeing HH first. Actually, a simpler way to see this is using a state machine or the Penney's Game formula. Expected wait time for HHT is 8. Expected wait time for HTH is 10. Wait, Penney's Game rules are non-transitive. Let's look at the prefix.

Winning prob for A (HHT) vs B (HTH):
If we see T first, we are back to start.
If we see HH, A wins effectively (guaranteed).
If we see HT, we are on track for B.
Detailed derivation available in the full course.

Frequently Asked Questions

Yes. We aggregate questions from recent interview candidates at firms like Jane Street, Citadel, and HRT. We verify them against our internal database of known question types.

For Quant Developer roles, C++ is often required or strongly preferred. For Quant Trader roles, Python is usually sufficient, but C++ familiarity is a bonus. Our platform supports both.

We categorize questions into Easy (sanity checks), Medium (standard interview level), and Hard (competitive/final round). We recommend starting with Medium.

Yes! We have a 'Fundamentals' track designed for those new to quantitative finance. It covers the basic probability and statistics concepts you need before tackling harder problems.