Compute probability two arrivals meet within 15 minutes
Company: Agoda
Role: Software Engineer
Category: Software Engineering Fundamentals
Difficulty: medium
Interview Round: Technical Screen
### Probability puzzle
Two people plan to meet, but they arrive independently at a random time within the next **1 hour**.
- Person A’s arrival time is uniformly random in
\( [0, 60] \) minutes.
- Person B’s arrival time is uniformly random in
\( [0, 60] \) minutes.
- They **meet** if the absolute difference between their arrival times is **at most 15 minutes** (i.e., they are both present within a 15-minute window of each other).
**Question:** What is the probability that they meet?
(Assume arrival times are continuous and independent.)
Quick Answer: This question evaluates understanding of continuous probability and geometric probability, focusing on independent uniform random variables and reasoning about time-window overlap.