Assume the probability of each relay being closed is p and that each relay is open or closed independently of other relay. What is the probability that current flows from L to R?
This is a problem of relaibility analysis of meshed system. You have three paralell branches with relays: First branch is R1 II R2 in serie with R3. Second branches is R4 and third branch is relay R5 in serije R6. Now you need to use formula from components relaibility jn serie and parralell connections to compute probability. You can find in any literature from Roy Billinton.