I want to check the following theorem by using Mathematica:

$\textbf{Theorem} $. If three point $P,Q,R$ are picked independently at random in the triangle $ABC$, than expected value of the area of triangle $PQR$ is

$S_{PQR}=\frac{1}{12}S_{ABC}$

I tried:

first I define triangle $ABC$ with area $S_{ABC}$

triangle = Triangle[{{0, 0}, {1, 1}, {2, 0}}];

area = Area[triangle]

but I don't know how to define new random triangle (random three point) inside the $ABC$ triangle.

I want to do something like this

t1=Graphics[{Red,triangle}]
t2=Graphics[{Black, rundomtriangle}]
Show[t1,t2]

than

S1=Area[triangle]
S2=Area[randomtriangle]

$\frac{S1}{S2}$ is a random number.

than plot this random numbers

ListPlot[S1/S2, S1/S2, S1/S2,...}]

but.. how to define randomtriangle ?