Consider the following events :
A = Switch S1 works,
B = Switch S2 works,
We have,
(i) The circuit will work if the current flows in the circuit. This is possible only when both the switches work together.
Therefore, Required probability
(ii) The circuit will work if the current flows in the circuit. This is possible only when at least one of the two switches S1, S2 works.
Therefore, Required Probability