MathDB

Six cities

A, B, C, D, E

, and

F

are located on the vertices of a regular hexagon in that order.

G

is the center of the hexagon. The sides of the hexagon are the roads connecting these cities. Further more, there are roads connecting cities

B, C, E, F

and

G

, respectively. Because of raining, one or more roads maybe destroyed. The probability of the road keeping undestroyed between two consecutive cities is

p

. Determine the probability of the road between cities

A

and

D

is undestroyed.

Problem Statement