Please break the solution into more steps to help me understand.

An actuary has discovered that policyholders are three times as likely to file two claims
as to file four claims.
If the number of claims filed has a Poisson distribution, what is the variance of the
number of claims filed?
(A) 1
3
(B) 1
(C) 2
(D) 2
(E) 4

Solution to be broken down further:

Solution: D
Let N be the number of claims filed. We are given P[N = 2] =
2 4
3
2! 4!
e e
 = 3  P[N
= 4]24 2 = 6 4
2 = 4 " = 2
Therefore, Var[N] = = 2 .

Here are the urls to the sample questions below:
http://www.soa.org/Files/Edu/edu-exam-p-sample-quest.pdf
http://www.soa.org/Files/Edu/edu-exam-p-sample-sol.pdf