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This question is commonly asked for Data Scientist candidates at SIG (Susquehanna) during technical interviews.

Infer posterior after losing pick

Last updated: Mar 29, 2026

Quick Overview

This question evaluates a candidate's understanding of conditional probability and posterior inference, assessing the ability to update probability estimates after observing that a chosen option did not occur.

SIG (Susquehanna)

Aug 11, 2025, 12:00 AM

Data Scientist

Take-home Project

Statistics & Math

Conditional probability after observing a loss

You have three cats in a jumping contest:

Cat 1 (most athletic) wins with probability p1
Cat 2 (middle) wins with probability p2
Cat 3 (least athletic) wins with probability p3

with p1 + p2 + p3 = 1.

You pick a cat uniformly at random (each with probability 1/3) to cheer for before the contest. After the contest, you learn that your chosen cat did not win.

Assuming your choice does not influence the outcome, what is the probability that you had picked the most athletic cat?

Solution

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