Students Not Majoring in English or History

This probability puzzle is about combining overlapping groups of students and working out how many are left outside both categories. It captures a very standard theme in quant interviews and quant prep: reasoning about events that can occur separately, together, or not at all, and interpreting given percentages as probabilities of membership in sets.

It trains comfort with basic set algebra, event unions and intersections, and complements. You practice translating a word description of majors into events, keeping track of overlaps, and turning raw percentages into consistent probabilities. It also reinforces careful reading, since a small change in wording about "both" or "neither" can alter the required calculation.

This matters for quant interviews because many market, risk, and data questions boil down to overlapping events: joint default, co-movements, scenario combinations, and coverage gaps. Recruiters use it to check whether you can quickly structure simple probability problems without confusion or double-counting, which is crucial in trading, risk, and research roles.

What it tests

Whenever you are asked for the total size of a union of overlapping groups, you must account for the overlap to avoid double-counting. The inclusion-exclusion principle provides a systematic way to do this: for two sets, the union's size is the sum of the sizes of each set minus the size of their intersection. This pattern arises because each member of the intersection is counted once in each group, so it is counted twice in the naive sum. Subtracting the intersection corrects this overcount, ensuring each individual is counted exactly once. This principle generalizes to more sets, with alternating sums and subtractions for higher-order intersections, but the core idea is always to adjust for overcounting by considering overlaps.