At an urgent care facility, patients arrive at an average rate of one patient every seven minutes. Assume that the duration between arrivals is exponentially distributed.

a. Find the probability that the time between two successive visits to the urgent care facility is less than 2 minutes.

b. Find the probability that the time between two successive visits to the urgent care facility is more than 15 minutes.

c. If 10 minutes have passed since the last arrival, what is the probability that the next person will arrive within the next five minutes?

d. Find the probability that more than eight patients arrive during a half-hour period.