The 13 Bridges Problem

Problem statement:

A river has six islands connected by a system of bridges as shown to the right (islands and river banks are green, bridges are gray). A flood has destroyed some bridges: each bridge is destroyed with probability 1/2, independent of the others. What is the probability that after the destruction one can cross the river from left bank to right using the remaining bridges?

Hint show

Solution show

This is one of several pages on using symmetry in mathematics.