Q.

A customer comes to a gas station at a rate of one every five minutes. what is the probability

(a) that no one comes for 5 mins

(b)that at least 3 cars come during five minutes!??

i know it is poisson but in (a) i dont know what lamda is and why?

and in

(b) i have 1-[e^(-lamda.t)]-[lamda.t.e^(-lambda.t)]-[1/2(lambda.t)^2.e^(-lambda.t)]

that is the answer in the book but I don't see why the "t" is brought down , do you differentiate it or something???