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Two individuals, A and B, plan to meet at a location sometime between 5:00 p.m. and 6:00 p.m. The person who arrives first waits for 20 minutes before departing. Assuming their arrival times are independent and uniformly distributed, what is the probability that they encounter each other?
- 1/3
- 4/9
- 5/9
- 2/3
Correct answer: 5/9
Solution
For meeting within a waiting time t over an interval T, P = 1 - ((T-t)/T)^2 = 1 - (40/60)^2 = 1 - 4/9 = 5/9, option (c). The stored answer 1/3 is incorrect.
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