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# Probability of encounter on trip

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Lets say you have a person traveling along some path from point A to point B. Lets also say that between points A and B are various wolf packs. You have some chance of encountering a wolf depending on where you are and the concentration of the wolf packs. To illustrate my question, here is a simple map. The gray line shows the path taken from point A to point B. The red contours indicate a region where there is some probability of encountering a wolf (the probability is denoted by the number). On the example map, the person starts his travels in a region where there is only a 5% chance of encountering a wolf. Then he moves into a region where there is a 61% chance of encountering a wolf, and so on. My question is how many wolves (and where) will the person encounter on his trip from point A to point B? Thanks for your help. [edited by - spiffgq on January 23, 2003 4:38:06 PM] [edited by - spiffgq on January 23, 2003 4:38:46 PM]

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Anywhere between 0 and an arbitary constant.

I think you need to explain your problem a bit better.

A way to work out the probabilities of encountering various numbers of wolves isn't too hard to work out.

Work out the distance travelled in each zone so you can work out how many checks you need to perform against the probability of that region.

Use the number of permutations and calculate the probability of each one. Then you have to combine each probability with the probability in the next leg of the journey. You get long long equations but will have a very accurate result.

[edited by - Metorical on January 23, 2003 4:49:10 PM]

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quote:
Original post by Metorical
Anywhere between 0 and an arbitary constant.

I think you need to explain your problem a bit better.

A way to work out the probabilities of encountering various numbers of wolves isn''t too hard to work out.

Work out the distance travelled in each zone so you can work out how many checks you need to perform against the probability of that region.

Use the number of permutations and calculate the probability of each one. Then you have to combine each probability with the probability in the next leg of the journey. You get long long equations but will have a very accurate result.

This sounds something like I was thinking. But I figured there had to be a time variable in there somewhere. If the person spends 1 second in one part of the leg and 1 year in another, it seems like that would affect the probability, too.

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You would need to specify the total number of wolves. The problem becomes much easier if you assume that the wolves are motionless, and so staying at one spot for an indefinite amount of time would not change the number of wolves encountered. Moreover, even if you allow for the wolves to be in motion, you need to understand that it's not the _probability_ that changes with time, it's the number of wolves encountered.

Simply specifying a probability for each zone implies what the chances are of encountering a wolf in some area, not in some time period. If you wanted to apply a probability distribution onto a temporal dimension as well, just make each zone's respective probability as a function of time spent in that zone.

[edited by - Hyprlogik on January 23, 2003 6:56:03 PM]

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HyprLogik has touched on the important issue here... what do your probabilities represent? Once you have determined this, then working out how many wolves encountered is fairly trivial.

Does the probability of a region, let''s call it p, represent the chance per time interval (second, minute, hour, or whatever) of encountering a wolf? In which case, the number of wolves encountered is simply p*dt, where dt is the time spent in that region.

Alternatively, does p represent the probability of encountering a single wolf while passing through that region? In which case, you''ll encounter 1 wolf 100*p% of the time and no wolves 100*(1-p)% of the time. If you pass through the region n times, then you would expect to encounter n*p wolves.

Finally, p might reprent the probability of meeting a wolf for every distance unit traveled (meter, kilometer, etc). The number of wolves met will be p*d, where d is the total distance traveled within that region.

I hope all of this makes sense for you.

Good luck,

Timkin

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