30. Three marksmen take turns shooting at a target. Marksman 1 shoots until he misses, then Marksman

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30. Three marksmen take turns shooting at a target. Marksman 1 shoots until he misses, then Marksman 2 begins shooting until he misses, then Marksman 3 until he misses, and then back to Marksman 1, and so on.

Each time Marksman 1 fires he hits the target, independently of the past, with probability Pi9 i = 1, 2, 3. Determine the proportion of time, in the long run, that each Marksman shoots.

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