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        riddles >> medium >> The hunter and the most likely dead fox 
        
(Message started by: apsurf on Apr 23^rd, 2005, 6:45pm)

Title: The hunter and the most likely dead fox
Post by apsurf on Apr 23^rd, 2005, 6:45pm

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.

Title: Re: The hunter and the most likely dead fox
Post by markr on Apr 23^rd, 2005, 7:58pm

[hide]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[/hide]

edit: added missing right paren noted below

Title: Re: The hunter and the most likely dead fox
Post by Grimbal on Apr 25^th, 2005, 12:59am

I agree, but there is a ')' missing after 4.5.