13 Bridges

Imagine that there six islands in a river that flows through a city, and there are 13 bridges connecting the North and South banks of a river and the islands as shown below:

             North Bank
     ###########################
        |         |         |
        O---------O---------O
        |         |         |
        O---------O---------O
        |         |         |
     ###########################
             South Bank

Suppose there’s a storm one night, and each bridge has a 50% chance of collapsing (independent of what happens to the other bridges).

What’s the probability that it will be possible to cross the river from the North bank to the South bank using the bridges remaining after the storm?

Solution