Compute probability of random arithmetic progression triple
Overview
This question evaluates combinatorics and probability skills, specifically counting combinations and recognizing arithmetic progression structure among distinct integers, and belongs to the Coding & Algorithms category for Data Scientist roles.
Mavensecurities
Nov 20, 2025, 12:00 AM
Data Scientist
Take-home Project
Coding & Algorithms
0
0
You have the integers from 1 to 30 inclusive.
You randomly choose 3 distinct numbers without replacement, and all 3-element subsets are equally likely. The order in which the numbers are drawn does not matter.
What is the probability that these three numbers can be arranged to form an arithmetic progression (three distinct terms with a common difference)? Express your answer as a simplified fraction or decimal.