ILL 1990 Problem 13

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.