A sequence of queries are made to a database system. The response time of the system,

$$ seconds, is an exponential random variable with mean $8.$ As soon as the system

responds to a query, the next query is made. Assuming the first query is made at time

zero, let $()$ denote the number of queries made by time $.$

a$)$ What is $(>=4),$ the probability that a single query will last four seconds?

b$)$ If the database user has been waiting five seconds for a response, what is

$>=13>=5,$ the probability that it will last at least eight more seconds?