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SEAMO 2027 - Paper E - SET 08 - Self-study Question 23

SEAMO · SEAMO 2027 - Paper E - SET 08 - Self-study

Question 23

Two people arrive at the same swimming pool at random times between 2:00 PM and 5:00 PM, and each swims for one hour. What is the probability that they meet?

Assume the two arrival times are independent and uniformly distributed over the three-hour interval. Each stays a full hour, even if departure is after 5:00 PM.
  1. $\frac19$
  2. $\frac29$
  3. $\frac13$
  4. $\frac49$
  5. $\frac59$