Matching Balls from Two Jars

This combinatorics question sits at the intersection of basic counting and introductory probability, a core theme in quant prep for interviews. It turns a simple color setup into a clean probability model with independent draws, which is exactly the kind of scenario that appears again and again in quant interviews, brainteasers, and online assessments.

It trains your ability to translate a verbal description into events, recognize independence, and structure the "match" outcome into mutually exclusive cases. It also reinforces comfort with proportional reasoning, joint probabilities, and simple law-of-total-probability thinking under time pressure.

It matters for quant interviews because many harder questions at banks and hedge funds are just richer versions of this pattern. Interviewers use this style of exercise to see whether you can quickly set up events, avoid double-counting, and compute clean, numerical answers without hand-holding.

What it tests

When dealing with independent random selections from separate groups, the probability that two outcomes share a property (such as color) is found by considering each matching scenario separately and summing their probabilities. This is an application of the law of total probability, where the 'match' event is partitioned into mutually exclusive cases (e.g., both red or both blue). For each case, the joint probability is the product of the individual probabilities, since the draws are independent. The sum of these products gives the total probability of a match. This approach works because independence lets us multiply probabilities, and the cases are exhaustive and exclusive, ensuring we count every way a match can occur without overlap.