A probabilistic way to discover the rainbow

TL;DR

This paper introduces a probabilistic approach using spatial random walks to quantify the likelihood of identical Skittles packs and the expected number of purchases until a match occurs, making it educational for students.

Contribution

It presents a novel probabilistic framework for analyzing the similarity of randomly selected candy packs using spatial random walks.

Findings

Calculated probability of two packs being identical

Determined expected number of purchases until first match

Proposed an educational approach for students

Abstract

"No two rainbows are the same. Neither are two packs of Skittles. Enjoy an odd mix!". Using an interpretation via spatial random walks, we quantify the probability that two randomly selected packs of Skittles candy are identical and determine the expected number of packs one has to purchase until the first match. We believe this problem to be appealing for middle and high school students as well as undergraduate students at University.