Use random numbers to estimate π, based on the fraction of (x,y) points falling in a unit circle inscribed in the range of random numbers.

We can use the fraction of randomly generated Cartesian points falling in a quarter unit circle (area (π/4))sector to estimate π.

ApproxPi[
        n_]  := 
Length[
Select[
Sqrt[
Apply[
Plus, 
Table[
                    Random[],  {n},  {2}]^2, 
{1}
]
], 
(#  ≤  1) &
]
]/(n/
            4)

ApproxPi[100000]  // N

Trace the steps in the above routine (for smaller sample size).

myTable  =  Table[Random[],  {10},  {2}]

%^2

Apply[Plus,  %,  {1}]

(This step is optional since (Sqrt[1]) =  1. )

Sqrt[%]

Select[%,  #  ≤  1  &]

Length[%]

%/Length[myTable]

4 %  // N