Three marksmen take turns shooting at a target. Marksman 1 shoots until she 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 shot of marksman i hits the target, independently of the past, with probability Pi, i = 1, 2, 3.

Determine the proportion of time, in the long run, that each marksman shoots.

Also, determine the proportion of shots that hit the target.