An insurer selects risks from a population that consists of 3 indep groups.

The claims generation process for each group is poisson.

The 1st group consists of 50% of the population. These individuals are expected to generate one claim per year.

The 2nd group consists of 35% of the population. These individuals are expected to generate two claims per year.

Individuals in the 3rd group are expected to generate three claims per year.

A certain insured has two claims in year 1.

What is the probability that this insured has more than two claims in year 2?

A. Less than 21%

B. At least 21%, but less than 25%

C. At least 25%, but less than 29%

D. At least 29%, but less than 33%

E. 33% or more

I got the answer was 23.98%, which is B. However, the answer sheet says the correct one is C.

I calculated the probabilities of the insured has more than two claims in year 2 for each group, then times the each groups' proportion of the population. I did not use the condition that the insured has two claims in year 1, since I think year 2 is indep with year 1. Is there anything wrong?

Thank you very much