Compute probability two arrivals meet within 15 minutes

Q: Compute probability two arrivals meet within 15 minutes

This question evaluates understanding of continuous probability and geometric probability, focusing on independent uniform random variables and reasoning about time-window overlap.

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Question

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.)

Compute probability two arrivals meet within 15 minutes

Quick Overview

Probability puzzle

Solution

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