Third in Line at the Bank
A bank has two tellers. When Carol walks in, Alice is being served by one teller and Bob by the other, and nobody else is waiting. Carol will be served by whichever teller becomes free first. All service times (Alice's remaining time, Bob's remaining time, and Carol's full service time) are independent exponential random variables with the same mean. What is the probability that Carol is the last of the three to leave the bank? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- Finishing in Order 4.0/10
- The Gap Between Two Lifetimes 4.0/10
- Twice as Long 3.0/10
Source: Classic exponential-distribution exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.