Couldn't solve one exercise. Exercise is as follows:
The Bank employs $10$ operators. The service time for each is exponentially distributed, with the average $i$-th operator serving $i$ clients per hour. The queue is single. By the beginning of work, Bob is the $20$th in the queue, the operators start serving at time $0$ simultaneously. Find the probability that Bob will get to the $7$th operator.
Help me understand the direction in which i need to solve this problem please.
The key property is that the exponential distribution is memoryless so just have to consider from the point when Bob gets to the front of the line. Now the total rate of serving is 55 customers per hour, so the probability that server 7 finishes first is $\frac{7}{55}$ and we are done.