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We study the dimension of “random” Euclidean sections of direct sums of normed spaces. We compare the obtained results with results from 
$[\text{LMS}]$, to show that for the direct sums the standard randomness with respect to the Haar measure on Grassmanian coincides with a much “weaker” randomness of “diagonal” subspaces (Corollary 1.4 and explanation after). We also add some relative information on “phase transition”.
