A family health insurance policy pays the total of the first three claims per year. If there is one claim during the year, the amount claimed is uniformly distributed between 100 and 500. If there are 2 claims in the year, the total amount claimed is uniformly distributed between 200 and 1000, and if there are 3 claims in the year, the total amount claimed is uniformly distributed between 500 and 2000. The probabilities of 0, 1, 2, and 3 claims in the year are 0.5, 0.3, 0.1, 0.1 respectively. Find the probability that the insurer pays at least 500 in total claims for the year.

If anyone knows how to solve this, please reply.

If anyone knows how to solve this, please reply.

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