How can i calculate the odds of a current passing in an electrical circuit in regards to a certain switch?

each switch is closed in 0.7 odds(and then electricity can be passed). also, each switch is working independently of others.

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1)if switch 3 is open(current not passing), what are the odds of current passing from a to b?

2)if switch 3 is closed, what are the odds of passing current from a to b?

so for 1, should it be (1 and 2) or (4 and 5) = (0.70.7) or (0.7 0.7) = 0.49 + 0.49 - 0.24? i think i still doing a mistake here and for 2, should it be (1 or 4) and (2 or 5) = (0.7+0.7-0.49)*(0.7+0.7-0.49)?

1 Answer
May 6, 2018

#"You got it correct !"#

Explanation:

#"I can confirm that your approach is completely correct."#

#"Case 1 : Switch 3 open (Probability 0.3) :"#
#0.49 + 0.49 - 0.2401 = 0.7399#

#"Case 2 : Switch 3 closed (Probability 0.7) :"#
#(0.7 + 0.7 - 0.49)^2 = 0.8281#

#"So the overall probability for the circuit that the current can"# #"pass is : "#

#0.3 * 0.7399 + 0.7 * 0.8281 = 0.80164#