Compute probability two arrivals meet within 15 minutes
Probability of Meeting
Two individuals, Person A and Person B, plan to meet. Their arrivals are independent and occur at a random time within a 60-minute window.
- Person A's arrival time is uniformly random within the interval [0, 60] minutes.
- Person B's arrival time is uniformly random within the interval [0, 60] minutes.
They are considered to have met if the absolute difference between their arrival times is at most 15 minutes.
Question: What is the probability that Person A and Person B meet?
Assume arrival times are continuous and independent.
AI interview prep
Core dilemma
Accurately modeling a continuous probability space and deriving a precise analytical solution under given constraints, translating a real-world scenario into a robust mathematical model.
3 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Compute probability two arrivals meet within 15 minutes
Probability of Meeting
Two individuals, Person A and Person B, plan to meet. Their arrivals are independent and occur at a random time within a 60-minute window.
- Person A's arrival time is uniformly random within the interval [0, 60] minutes.
- Person B's arrival time is uniformly random within the interval [0, 60] minutes.
They are considered to have met if the absolute difference between their arrival times is at most 15 minutes.
Question: What is the probability that Person A and Person B meet?
Assume arrival times are continuous and independent.