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Needed A Smart & Genius & Patient People Pleas To help me in solving this question for necessary, Ty .

Mathematics
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An ant stands in the middle of a circle (3 metres in diameter) and walks in a straight line at a random angle from 0 to 360 degrees. Problem is, it can only walk one metre before it needs a break. The ant has the memory of a fish and forgets what direction it has just walked in.. Anyway, after the break, it gets all dizzy and thus chooses another random direction from 0 to 360 in an attempt to escape the circle again. As you can well imagine, it could escape the circle after just 2 walks (just one break needed). Or... it could take 20,000 walks (19,999 breaks needed)!! There might even be the very slim possibility it might take 20,000^20,000 walks.... What is the average amount of walks required for the ant to escape the circle?
@TuringTest :My Native Language is German.. :) Would u mind to delete your recent comments to make sure every one can see it from the first view ?
is this a trick question. the highest amount of walks that the ant can do is \[\infty\] because it can continue to walk in circles foreer

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Other answers:

@Zarkon probability problem
@Outkast3r09 :Its not a tricky question .,Its has a definite answer .
this is way out of my league frankly
well lets see graphing it you get
though @Outkast3r09 makes a very convincing (to me) argument
|dw:1341367888952:dw|
lol
Is that the circle or its just a poker face @Outkast3r09 ?
|dw:1341367915879:dw| it's pacman
I believe it lacks a .5 as well..
o gahd i thought it said that the diameter was 2 metres
we need to find the probability that on the second walk what angles it needs to be -.-
right, so after the first walk it has some situation like|dw:1341368144531:dw|
Guys ,Sorry i need to close this question and repost it ,,,It makes me laggy :s
|dw:1341368212808:dw|what are the odds (what percentage of the possible directions) that he escapes the circle on the next move...maybe I dunno, I'm just thinking where to start

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