1 Suppose n and k are two positive integers Pick a uniforml...

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1 Suppose n and k are two positive integers  Pick a uniformlyrandom la...

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I am assuming you are just considering NorthEast lattice pathsie paths that only go up and right Then to go from 00 to nk via a lattice path you have to take n steps North and k stepsEast thus resulting in total of n k steps Then lattice pathsfrom 00 to nk is the same as choosing at which n of these n k steps you choose to go North and at the remaining k steps you areforced to go 1 step East nk Thus the required number of latticepaths is Of these total number of paths where the first step isup lattice paths ....

1.Suppose n and k are two positive integers. Pick a uniformly random lattice path from (0,...

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1.Suppose n and k are two positive integers. Pick a uniformlyrandom lattice path from (0, 0) to (n, k). What is the probabilitythat the first step is ‘up’?

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