Green & Blue in 4 Draws

This probability question is about counting outcomes efficiently when several different colors must all appear in a short sequence of draws. It sits at the intersection of basic combinatorics and discrete probability, which is core material in quant prep and shows up in many quantitative finance interviews. Candidates need to be comfortable moving between combinatorial reasoning and probabilistic interpretations under simple, clean assumptions.

It trains your ability to handle events that must each occur at least once, to recognize symmetry, and to translate a verbal condition into clean mathematical events. It also sharpens your intuition for independence across trials and for working with complements of events, which is a recurring pattern in quant interviews and technical screening tests.

This matters for a quant interview because modeling payoffs, risk events, or execution outcomes often reduces to similar counting and probability structures. Interviewers want to see that you can recognize when direct enumeration explodes, choose a smarter perspective, and keep track of overlapping cases without algebraic mistakes. Mastering questions like this builds the combinatorial reflexes needed for tougher quant interviews and online assessments.

What it tests

When a problem asks for the probability that multiple distinct events each occur at least once across several independent trials, the direct computation often involves complex casework due to overlapping possibilities. Instead, the principle of inclusion-exclusion allows us to efficiently compute the complement: the probability that at least one of the events does not occur. This works because the complement—missing at least one event—can be broken down into simpler, non-overlapping cases (missing each event individually, missing both, etc.), and the independence of trials makes these probabilities straightforward to calculate. The inclusion-exclusion formula corrects for overcounting the overlap between these cases, ensuring accuracy. This approach is especially powerful when the events are symmetric or when the complement cases are easier to enumerate than the original favorable cases.