Infer posterior after losing pick
Company: SIG (Susquehanna)
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Online Assessment
Three cats compete in a jumping contest. The most athletic cat wins with probability p1, the middle cat with probability p2, and the least athletic cat with probability p3, where p1 + p2 + p3 = 1. You pick a cat uniformly at random to cheer, but your chosen cat does not win. What is the probability you picked the most athletic cat?
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.