Under an insurance policy, a maximum of five claims may be filed per year by a policyholder. Let Pn 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 for

- PnPn+1 fo r n=0,1,2,3,4

- The difference between Pn and Pn+1 is the same for n = 0, 1, 2, 3, 4.

Exactly 40% of the policyholder files fewer than two claims during a given year.

Calculate the probability that a random policyholder will file more than 2 claim during a given year.