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I am stuck with the problem of solving this problem for my research.

I have 3 random variables say X, Y, and Z and say

Pr[X > Y] = p_xy, Pr[X > Z] = p_xz, and Pr[Y > Z] = 0.5.

Note that p_yx = 1 - p_xy. Similarly, p_zx = 1 - p_xz, p_yz = p_zy = 0.5

I need to find out the Pr[X > Y and X > Z] ?

Any directions to solve this problem would be of great help.