There are three tellers at the bank.

Slow Joe with exponential mean 5 minutes

Lightning Larry with exponential mean 1 minute.

Medium Mary with exponential mean 1.25 minutes.

Suppose you wait in queue behind people A who is at Lightning Larry and B who is at Medium Marry instead of going to Slow Joe.

1. What is your expected time in the system given that you chose not to enter service with Slow Joe? (expected time waiting + expected service time)

2. What is the probability You are second to complete service between You, Customer A, and Customer B?

3. What is the probability that You are the last one to complete service between You, Customer A, and Customer B?

4. A fourth customer, customer C, enters the bank while A and B are still in service. Recall, you are waiting in line, refusing to start service with Slow Joe. Customer C decides to begin service with Slow Joe. What is the probability You will complete service after Customers A or B before Customer C does with Slow Joe? (either A finishes the 3-way race first and then You finish the 2-way race before C or B finishes the 3-way race first and then You finish the 2-way race before C)