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In the case $n=3$ we prove that the average number of real lines on a random cubic surface in $\\mathbb{R}\\textrm{P}^3$ equals: $$E_3=6\\sqrt{2}-3.$$ Our technique can also be used to express the number $C_n$ of complex lines on a generic hypersurface of degree $2n-3$ in $\\mathbb{C}\\textrm{P}^n$ in terms of the determinant of a random Hermitian matrix. 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