Under an insurance policy, a maximum of of 5 claims may be filed per year by a policy holder. Let
p(n) be the probability that a policyholder files n claims during a given year, where n= 0,1,2,3,4,5. An actuary makes the following observations:
1) p (n) >= p (n+1) for 0<=n <=4
2) the difference between p (n) and p (n+1) is the same for 0 <= n <= 4
3) exactly 40% of policyholders file fewer than 2 claims during a given year.
Calculate the probability that a random policyholder will file more than three claims during a given year.
Can't seem to figure this one out. Any help would be great.