Q:

Calculating probabilities using multi-dimensional statistical distributions

Probability[Max[x,y]-Min[x,y]<1/3,{x,y}\[Distributed]UniformDistribution[{0,1}]]

Why doesn't Mathematica calculate this query? 
Probability[
 Max[x, y] - Min[x, y] < 1/3, {x, y} \[Distributed] 
  UniformDistribution[{0, 1}]]

A:

You should either specify a distribution for each variable:
 {x \[Distributed] UniformDistribution[{0, 1}], 
  y \[Distributed] UniformDistribution[{0, 1}]}

Or use a multivariate one:
 {x, y} \[Distributed] UniformDistribution[{{0, 1}, {0, 1}}

In this case it also equivalent to:
 {x, y} \[Distributed] UniformDistribution[2]

