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

Given:

`P(S_{1})=P(S_{2})=P(S_{3})=frac{1}{2}`


So, Let E be the event that the current will flow. Then,

`P(E)=P((S_{2} cap S_{3}) or S_{1}) `

`=P(S_{2} cap S_{3})+P(S_{3})-P(S_{1} cap S_{2} cap S_{3})`

`=frac{1}{4}+frac{1}{2}-frac{1}{8}=frac{5}{8}`