Time in post office
Question
A bank has 2 tellers. Andy enters the bank, while the two tellers are busy serving two other customers (Customer A and Customer B). Andy is next in line. The time a teller spends serving a customer has an Exponential(λ) distribution. Given this information:
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a) What is the probability that Andy is the last of the 3 customers to finish being served?
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b) What is the expected total time that Andy will need to spend at the bank?