Poisson distribution: buses stopping at a give stop

The number of buses that stop to pick up passengers at a given bus stop is known to be Poisson distributed with a mean of 7 per hour. Find the probability that:

At least one bus stops to pick up passengers in any given thirty minute period.

Somebody who arrives at the bus stop will have to wait more than fifteen, but not more than thirty, minutes for a bus.

There was no bus in the first fifteen minutes, given that there was exactly one bus in a thirty minute period.

I think this ispoisson distribution, could anybody please help with this I am very confused...

Re: poisson distribution

The first one is purely Poisson.
If the rates is 7/hr, doesn't this make it 3.5 / half hour?
Pr(at least one in 30 min) = 1-e^(-3.5) = 0.0302

For the second, you must come to grips with the EXPONENTIAL wait times of a Poisson Process.

Let's see what you get.