Random model lorenz curve of uplift curve

I built an uplift and cumulative gain charts curve and the benchmark is always a random model which is plotted at (0,0), (100%, 100%) (i e in an uplift model target 10 % of customers will provide 10% of positive responses , target 20% ​​of customers will provide 20% of positive responses and so on).Here is the behavior of a random model which select customers without any criteria for selection of customers .

I wanted to know why the random model is always in the form of y = x , how we know that a random model will always do the same

here is a photo of how random model works , it is the one in pink that cuts the curve in the middle

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I would be happy to have responses if anyone has a clear idea so that I can understand the idea behind (sorry for my poor english )

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