Compute probability two arrivals meet within 15 minutes
AgodaSoftware Engineer · Technical Screen
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This question evaluates understanding of continuous probability and geometric probability, focusing on independent uniform random variables and reasoning about time-window overlap.
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.)
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