Right. That makes sense in the contrived scenario (although in that contrived scenario we know the probabilities with absolute surety).
replyBut TFA's estimate is perplexing because it is NOT a contrived scenario. We don't have marbles, we have some territory to cover. The territory isn't randomly distributed, we can't adequately randomly sample (presumably?).
It feels like the estimate could be wildly wildly off, in which case why estimate.
The contrived scenario is just a starting point. One can make more and more sophisticated ecological statistics models about the situation.
replyRegarding why estimate at all knowing they can be wrong ? Estimates are very useful for planning. Sophisticated models would also yield probabilities of over and underestimated, these combined with cost of over and underestimation errors are very useful for decision making.
See the German tank problem. Turns out the allied forces overestimated the number to f tanks left, still helped in planning.
It also makes sense in non-contrived scenarios ... the contrivance was just pedagogical.
replyGreat explanation, thanks!
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