Two-Point Play Strategy

This interview question presents a late-game decision in a basketball scenario where a player must choose between two different scoring options, each leading to different downstream outcomes for the team. The candidate is asked to quantify which option gives a higher chance of ultimately winning, taking into account the direct result of the shot and the possibility of the game continuing. It is framed in everyday terms and is typical of probability and expected value questions used in entry-level quant interviews and general problem-solving screenings.

The problem leans on basic probability rules, especially multiplying probabilities along a sequence of events and then comparing overall success chances across paths. It requires recognizing that one option has a single-stage outcome while the other is a multi-stage path, and that both must be evaluated on the same footing as total win probabilities. An interviewer is looking for comfort with conditional reasoning, clear decomposition of cases, avoidance of intuitive but incorrect shortcuts, and the ability to translate a verbal scenario into a simple probabilistic model.

What it tests

Whenever a decision involves multiple stages with probabilistic outcomes, the total probability of a desired result is found by multiplying the probabilities along each possible path and summing over all mutually exclusive ways to achieve that result. This is an application of the law of total probability: break down the event of interest into disjoint cases, compute the probability for each, and add them up. The principle holds because each stage's outcome can be conditioned on the previous one, and the overall chance of success is the sum of the probabilities of all successful paths. This approach is essential when outcomes depend on both immediate and subsequent events, such as making a shot and then winning in overtime. It ensures that all possible scenarios leading to the goal are accounted for, weighted by their likelihood.