Deer Dilemma
In Kisatchie National Forest in Louisiana, where there are thousands of deer, one out of 10 on an average is a blackbuck (endangered species). If you happen to shoot at random 10 deer in this forest, what is the chance that you will have hit at least one blackbuck? And how many deer do you need to shoot to be sure with a confidence of 90 percent that a blackbuck has been shot?
Labels: Probability, puzzle
posted by Rajesh Lal at
9:26 AM
7 Comments:
This post has been removed by the author.
P(shooting at least one blackbuck) = 1 - P(shooting no blackbucks)
= 1 - (9/10)^10 = 0.6513...
To raise this probability to 0.9 we need to shoot n deer, where
0.9 = 1 - (0.9)^n => (0.9)^n = 1-0.9 = 0.1
so n = log(0.1)/log(0.9) = 21.854....
So you need to shoot at least 22 deer to be 90% confident
that you shot at least one blackbuck. You rotten swine, you!
I think that to shoot one endangered blackbuck could be 1/100. This would be because you are shooting randomly, the probability of the 2nd deer is still 1/10, and the 3rd - 1/10 and the 4th etc. So - 1% chance of hitting a blackbuck out of 10 shots....
To give yourself a 90% guarantee of shooting one blackbuck... keep shooting.
First of all, I am not a hunter and know very little about the coloration of blackbuck deer. However, if the blackbuck's coloration identifies it, then:
To shoot and ACTUALLY hit a deer, one would probably have to ACTUALLY see the deer. If one ACTUALLY sees the deer ... one would ACTUALLY know what color the deer is ... by waiting until a black deer is in one's rifle sight, one could increase one's chance of shooting a black deer to 100% ... thus needing to shoot only one deer to be assured of hitting a black one.
Hmmmmmm ... some deer are over-populated and need thinning ... glad I'm not one of the thinner-ers ... thinner-ers? I have may coined a new word!
Probability of shooting blackbuck
1-(9/10)^10=0.65132 or ~=65%
Answer: 65%
Number of deer to shoot to be 90% confident, blackbuck has been shot
0.9=1-(9/10)^n
0.1=(9/10)^n
n=log(0.1)/log(0.9)=21.854
must round up to whole number
n=22
Answer: 22
Lots of new puzzles have been posted lately, which is a good thing, but these recently posted problems are looking more and more like someone's high school homework.
Cam
Zaux - Deer thinner-ers in Scotlant are called cullers, or poachers depending upon which side of the law you are on...
Heh heh ... thinner-ers ... I like to apologize for that ...
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