24okkkkk.......soln hasnt struck me tooo......Me trying for more than 5 dayz..
If a rod is marked random at n points and divided at these points,the chance that none of the parts shall be greater than 1/n th of the rod is 1/nn
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14 Answers
62this one is bugging me for the last 2 days.. i cant think of a solution at all :(
Am still trying! :)
24
9note ; made some mistakes in exp that ive edited in end
edit : abv corresponds to div rod into n+1 regions
i wrongly wrote as n region
also the graphs r rong
wen , n =1 ,its line x+y = 1 in ist coordinate (so region prop to l)
wen, n =2 its plane x+y+z =1 in ist coordinate ( so region prop to l2)
similarly for any n , its region prop to l^n
9contd ..........
so P = cases of div rod into n+1 pieces for rod of lenght l/n / that of l
= (l/n)^n/ l^n = 1/n^n
62i dont agreee to your solution.. you have made a small error
|x|+|y|+|z| = 1 is the graph...
these are all planes... 8 of them..
so they will form a diamond like structure..
a cube with diagonal equal to? (for u to answer) :)
was out of my mind when i was posting this one :D
9no sir i don agree wit u
X + Y + Z = 1 will be graph with x , y , z >0
9nishant now sol seems to be right
even i was out of mind for drawin feasible region as sqr and volumes
62celestine i forgot to post this one last nite.. i had the solution in mind..
see for a 3d case it will be a cube of side 1/3 from the origin in the 1st quadrant
and the overall part will be by the plane x+y+z=1
so the probability will be given by the volume ratio...
I dnot knwo if this is what you mean :)
9no its not volume ratio for n=2
its area ratio
see my edit abv