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Apr 17, 2015 at 21:17 vote accept domotorp
Apr 17, 2015 at 21:10 comment added Gregory J. Puleo It seems to me that you can cash this out formally in terms of the assignment version of the problem by taking all $x(E_i)$ and $x(A)$ equal to $1/2$, and taking the ordering so that the center vertex is minimal. Now to satisfy the hypothesis in the question we just need all $P[E_i] \leq 1/4$ and $P[A] \leq 1/2$, which as you say is easy to arrange.
Apr 17, 2015 at 20:51 history edited Aravind CC BY-SA 3.0
added 8 characters in body
Apr 17, 2015 at 20:34 history answered Aravind CC BY-SA 3.0