  A cubic hypersurface in $\mathbb{P}^n$ defined over $\mathbb{Q}$ is given by
the vanishing locus of a cubic form $f$ in $n+1$ variables. It is conjectured
that when $n \geq 4$, such cubic hypersurfaces satisfy the Hasse principle.
This is now known to hold on average due to recent work of Browning, Le Boudec,
and Sawin. Using this result, we determine the proportion of cubic
hypersurfaces in $\mathbb{P}^n$, ordered by the height of $f$, with a rational
point for $n \geq 4$ explicitly as a product over primes $p$ of rational
functions in $p$. In particular, this proportion is equal to 1 for cubic
hypersurfaces in $\mathbb{P}^n$ for $n \geq 9$; for $100\%$ of cubic
hypersurfaces, this recovers a celebrated result of Heath-Brown that
non-singular cubic forms in at least 10 variables have rational zeros. In the
$n=3$ case, we give a precise conjecture for the proportion of cubic surfaces
in $\mathbb{P}^3$ with a rational point.
