MathDB

Gunmay picks

6

points uniformly at random in the unit square. If

p

is the probability that their convex hull is a hexagon, estimate

p

in the form

0.abcdef

where

a,b,c,d,e,f

are decimal digits. (A convex combination of points

x_1, x_2, \dots, x_n

is a point of the form

\alpha_1x_1 + \alpha_2x_2 + \dots + \alpha_nx_n

with

0 \leq \alpha_i \leq 1

for all

i

and

\alpha_1 + \alpha_2 + \dots + \alpha_n = 1

. The convex hull of a set of points

X

is the set of all possible convex combinations of all subsets of

X

Estimation