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Topic: The hunter and the most likely dead fox (Read 1390 times) |
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apsurf
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The hunter and the most likely dead fox
« on: Apr 23rd, 2005, 6:45pm » |
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A hunter shoots from a distance of 100 yards at a fox running away from him: suppose that the probability that he hits it at this distance is 1/2. If he misses, the hunter reloads his rifle and shoots again, but in the time it takes to do this the fox runs 50 yards. If he misses a second time, he reloads the rifle and shoots a third (and last) time, the fox having meanwhile run another 50yards. Under the hypothesis that the probability of a hit is inversely proportional to the square of the distance, determine the probability that the hunter succeeds in hitting the fox.
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markr
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Re: The hunter and the most likely dead fox
« Reply #1 on: Apr 23rd, 2005, 7:58pm » |
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probability of hitting the fox =
1 - probability of missing all three shots =
1 - ((1 - 1/2) * (1 - 1/4.5) * (1 - 1/8)) =
1 - (1/2 * 3.5/4.5 * 7/8) =
95/144
edit: added missing right paren noted below
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| « Last Edit: Apr 25th, 2005, 7:48pm by markr » |
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Grimbal
wu::riddles Moderator
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Re: The hunter and the most likely dead fox
« Reply #2 on: Apr 25th, 2005, 12:59am » |
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I agree, but there is a ')' missing after 4.5.
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