Exercise: Bank tellers

$1$ point possible $($graded$)$

When you enter your bank, you find that there are only two tellers, both busy serving other customers, and

that there are no other customers in line. Assume that the service times for you and for each of the

customers being served are independent identically distributed exponential random variables. Also assume

that after a service completion, the next customer in line immediately begins to be served. What is the

probability that you will be the last to leave? Hint: Think of the situation at the time that you start getting

served.