For each of the following three scenarios, do the following

1.) Define a random variable for what the question is referring to.
2.) Write down the distribution of the random variable using the X ∼ notation, giving the parameter value(s).
3.) Write down a probability statement in terms of the random variable, P(X ≤ · · ·) etc, for what the question of interest is. You do not have to find the probability

(a) Scenario 1
In a town, there is a stop sign that 85% of cars make a complete stop at. A police officer starts watching cars go through the stop sign. What is the probability more than three cars go by before one that doesn’t completely stop at the stop sign?
(b) Scenario 2
A student takes a 20 question multiple choice exam where each question has four possible answers. The student will randomly guess on every question. What is the probability the student gets at most eight questions correct?
(c) Scenario 3
At a certain Bank, customers arrive at an average rate of 16 per hour. What is the probability that exactly 14 customers arrive between 1:00pm and 2:00pm on a random day?