Mathematics

Problem

An irrigation network has a 'Bridge' topology: Switches

A

and

B

are on the top left and right;

C

and

D

are on the bottom left and right; Switch

E

connects the midpoint of

AB

to the midpoint of

CD

. If switch

E

is permanently stuck OPEN (probability of conduction

= 0

), and all other switches (

A

B

C

D

) have probability

p=0.8

, calculate the probability that water flows from the left source to the right destination.