Quant Trading Interview Math: Expected Value, Probability Puzzles & Market Making

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Price three interview games by expected value: one die roll, a die with an optional reroll, and a card draw you are offered at a fixed price.
• Solve two classic interview puzzles with a Bayes table: which coin did you draw after five heads, and what is on the hidden side of a card?
• Build the step table of the geometric distribution, read off the chance of a win within k rolls and answer two favourite questions: the expected wait for a six, and for two sixes in a row.
• Measure the edge and the risk of a 2-to-1 bet, size it with the Kelly criterion and see in a growth table why betting twice Kelly earns almost nothing and more loses money.
• Price a call and a put on a die roll, check put-call parity and value a call on a two-flip coin tree, the way interviewers introduce options.
• Replay twelve customer trades against your two-sided quote: the price of each fill, your running inventory, cash and marked-to-market P&L, and a chart of the inventory you had to carry.
• Turn a classic estimation question into a chain of factors with low, base and high cases, find the midpoint on a log scale, round to a power of ten and size the revenue.
• Check three kinds of mental-math answers with formulas, percentage changes, compounding against the rule of 72, and a cumulative P&L, and chart the P&L path of a simulated strategy.