An electrical system has open-closed switches $S_1,S_{2}and{S}_3$ as shown in fig. The switches operate independently of one another and the current will flow from $A\to B$ either if $S_1$ is closed or if both $S_{2}and{S}_3$ are closed. If $P\left(S_1\right)=P\left(S_2\right)=P\left(S_3\right)=1/2,$ then find the probability that the circuit will work. fig

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