[Python] how to generate random probability arrays with pre specified mean

I have a pre specified mean [0.5, 0.5, 0]. This is a probability array which sum up to 1.

I want to generate several, say 10 random probability arrays (each sums up to 1) whose mean is [0.5, 0.5, 0], for example

out = [[1.41439945e-01 8.58560055e-01 0.00000000e+00]
[9.99967956e-01 3.20439716e-05 0.00000000e+00]
[9.42136832e-01 5.78631675e-02 0.00000000e+00]
[4.40349524e-01 5.59650476e-01 0.00000000e+00]
[7.44887609e-01 2.55112391e-01 0.00000000e+00]
[2.02038298e-01 7.97961702e-01 0.00000000e+00]
[2.87313048e-02 9.71268695e-01 0.00000000e+00]
[4.49155118e-01 5.50844882e-01 0.00000000e+00]
[9.99805466e-01 1.94534222e-04 0.00000000e+00]
[5.14967660e-02 9.48503234e-01 0.00000000e+00]]

np.mean(out, axis=0) # [0.5, 0.5, 0]



I first generate arrays using arrays = np.random.dirichlet((0.3,0.3,0.3), size=10), such that each row has a sum of 1, but how can I match with the mean?

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