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  • $\begingroup$ Presumably the distributions of a,b,c and d are linked together. I don't see any such links in your code. To me it looks like you have independent a,b,c,d (from the correct OrderDistributions) when they should be linked. Presume this is why NProbability gives the wrong answer (Probability would give the same but is slower). $\endgroup$ Commented Jan 5, 2014 at 16:14
  • $\begingroup$ @Ymareth I came to the same conclusion, e.g. a must be greater then b. $\endgroup$ Commented Jan 5, 2014 at 16:17
  • $\begingroup$ @Ymareth and ybeltukov doesn't the fact that it is distributed in f(15) do that? That is the maximum. $\endgroup$ Commented Jan 5, 2014 at 16:19
  • $\begingroup$ A possible simulation is num = 10^6; samp = (Sort /@ RandomVariate[UniformDistribution[], {num, 15}])[[All, -4 ;; -1]]; N@Length@Select[samp, Tr@# > 3.5 &]/num The result agrees with the OP's $\endgroup$ Commented Jan 5, 2014 at 17:01
  • $\begingroup$ @belisarius - Agrees with the stated correct answer but how in the OP's code do I know that the f[15] is always greater than f[14]. In your answer you have that implicitly as you're using the joint distribution but in the OP's code there are just 4 independent distributions - unless I'm misreading? $\endgroup$ Commented Jan 5, 2014 at 18:07