I would like to kindly know if there's anyone out here who can help me solve this problem..

COURSE 1 Nov 2001 # 32

The number of injury claims per month is modeled by a random variable N with

P[N = n] = 1/(n + 1)(n + 2)

, where n ≥ 0 .

Determine the probability of at least one claim during a particular month, given

that there have been at most four claims during that month.

(A) 1/3

(B) 2/5

(C) 1/2

(D) 3/5

(E) 5/6

Please explain your solutions as well as i dun know from where 1/6 +1/12+1/20+1/30(based on solution) come from...thank you very much...