Camden, New Jersey has on of the highest crime rates in the United States. As a result a new Camden County Police department will include 400 officers and be responsible for an area covering nine square miles. Suppose the number of times a police cruiser from this new department drives through the Whitman Park neighborhood during 1 hour perioud is a random variable, X, with probability distribution given in the table below:

x 0 1 2 3 4 5 6 7
p(x) 0.3679 0.3679 0.1839 0.0613 0.0153 0.0031 0.0005 0.0001
(a) What is the probability that at most two police cruisers will drive through the neighborhood?
(b) Suppose at least two police cruisers were sighted in the neighborhoof during the one hour period. What is the probability that there were at least four during this time?

(a) To get the probability that at most two police cruisers the neighborhood we have to consider the probability, of having 2 police, 3 police , 4 police , 5 , 6 or 7 police. All that possibilities meet my condition,

We have to add the probalities of the different possibilities to know the total probability

P=0.1839 +0.0613 +0.0153 +0.0031+ 0.0005 +0.0001=0.2642‬

(b) If we suppose that 2 police sighted in the neighborhoof and we are looking the probability of having 4 police , that means that 2 o more are random distribuited,

So, again , the probabily we are looking for is to have 2 o more police. Is the same calculus we made in the previus exercice.