Truck arrivals at a terminal follow a Poisson process with an average of 2 trucks per hour.

1)Determine the probability that there will be at least three truck arrivals in the next 30 minutes.

2)Consider the scenario where a truck has just arrived at the terminal. An employee wants to make sure he has enough time to take a break. Let T be the waiting time (in hours) before arrival of the next truck. Determine the probability that this employee can take a 15 minute break, that is, calculate P (T> 0.25).

3) In (2), What is the probability that this employee expects more than an hour, knowing he's already waited 15 minutes?