An electrical system has open-closed switches `S_1, S_2a n dS_3` as shown in fig. The switches operate independently of one another and the current will flow from `AtoB` either if `S_1` is closed or if both `S_2a n dS_3` are closed. If `P(S_1)=P(S_2)=P(S_3)=1//2,` then find the probability that the circuit will work. fig

Explanation

To solve the problem, we need to find the probability that the electrical circuit will work given the conditions of the switches. Let's break this down step by step.

### Step 1: Understand the conditions for the circuit to work
The circuit will work if:
1. Switch \( S_1 \) is closed, or
2. Both switches \( S_2 \) and \( S_3 \) are closed.

### Step 2: Define the events
...