Probability Help:

In modeling the number of claims filed by an individual under an insurance policy during a three-year period, an actuary makes the simplifying assumption that for all integers n\geq 0, \; p_{n+1}=\frac{1}{10} \; p_{n}, where p_{n} represents the probability that the policy holder files n claims during the period. Under this assumption, what is the probability that a policy holder files less than 3 claims during the period?

Question

Probability Help:

In modeling the number of claims filed by an individual under an insurance policy during a three-year period, an actuary makes the simplifying assumption that for all integers n\geq 0, \; p_{n+1}=\frac{1}{10} \; p_{n}, where p_{n} represents the probability that the policy holder files n claims during the period. Under this assumption, what is the probability that a policy holder files less than 3 claims during the period?

anonymous · Answer

$$n \ge 0, P _{n+1}=\frac{ 1 }{ 10 }P _{n}$$

anonymous · Answer

So I get that we need to find P[n<3], and but how do we find P[n=0]?

anonymous · Answer

nevermind. figured it out.