How can I find the probability that each coordinate of a specified multivariate normal distribution is positive? I tried the following, which I believed should work

mu = {0, 0, 0};
sigma = {{2, 1, 1}, {1, 2, 1}, {1, 1, 2}};
Probability[
 x > 0 && y > 0 && z > 0, {x, y, z} \[Distributed] 
 MultinormalDistribution[mu, sigma]]

Unfortunately, for the output I just get the last line from the input (with mu and sigma replaced by their actual values). I don’t see where the problem could possibly be since the matrix is positive definite. If I replace it by the identity matrix everything works fine.

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