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
Text Solution
Verified by Experts
` P(S_(1))=P(S_(2))=(S_(3))=1/2` Let E be event that "the current will flow". `P(E)=P((S_(2)nnS_(3))nnS_(1)))` `=P(S_(2)nnS_(3))+P(S_(3))-P(S_(1)nnS_(2)nnS_(3))` `P(S_(2))P(S_(3))+P(S_(3))-P(S_(1))P(S_(2))P(S_(3))` `=(1)/(2).(1)/(2)+(1)/(2)-(1)/(2).(1)/(2).(1)/(2).=5/8`
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