A merchant finds that 20% of customers ask for an item which is not in stock.
Customers arrive according to the conditions for a Poisson process with an
average rate of 12 per hour.

(1) Find the probability of 5 customers arriving in a 10-minute period.
(2) Find the probability 3 customers ask for an item that is not in stock, out of 20 customers at the store.
(3) Find the probability the xth customer arriving at the store is the 3rd to ask for an item which is not in stock.
(4) Give an expression for the probability that 3 customers will ask for an item that is not in stock during a 75-minute period.


for 1. i think it is f(5) = (2^5*e^-2) / 5!

for 2. i think it is (20 Choose 3)*(0.2)^3*(0.8)^17

for 3, i think it is ((x-1)choose 2)* (0.2)^3*(0.8)^(x-3)

i am not sure how to do 4
thanks a lot