Question

An electrical system has open-closed switches S₁, S₂ and S₃ as shown in Figure.
The switches operate independently of one another and the current will flow from A and B either if $S_1$ is closed or if both $S_2$ and $S_3$ are closed. If $P\left(S_1\right)=P\left(S_2\right)=P\left(S_3\right)=\frac{1}{2}$, then find the probability that the circuit will work

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$P\left(S_1\right)=P\left(S_2\right)=P\left(S_3\right)=\frac{1}{2}$
Let E be the event that the current will flow. Then,
$P\left(E\right)=P\left(\right(S_2\cap S_3\left)or{S}_1\right)=P(S_2\cap S_3)+P\left(S_3\right)-P(S_1\cap S_2\cap S_3)=\frac{1}{4}+\frac{1}{2}-\frac{1}{8}=\frac{5}{8}$