Electrical engineering probability: It is given that the probability of failure

Question

Electrical engineering probability: It is given that the probability of failure of a single resistor of value R, regardless of value, is a tenth of a percent (0.001). For each configuration, sketch the resistor network and find the probability of failure.
a) two resistors of value R/2 each, in series b) two resistors of value 2R each, in parallel c) four resistors of value R each in a series-parallel configuration Electrical engineering probability: It is given that the probability of failure of a single resistor of value R, regardless of value, is a tenth of a percent (0.001). For each configuration, sketch the resistor network and find the probability of failure.
a) two resistors of value R/2 each, in series b) two resistors of value 2R each, in parallel c) four resistors of value R each in a series-parallel configuration Electrical engineering probability: It is given that the probability of failure of a single resistor of value R, regardless of value, is a tenth of a percent (0.001). For each configuration, sketch the resistor network and find the probability of failure.
a) two resistors of value R/2 each, in series b) two resistors of value 2R each, in parallel c) four resistors of value R each in a series-parallel configuration

Explanation / Answer

(a) In a two resistor of value R/2 in series will give an equivalent of a single R resistor. But the probability of failure of a resistor is 0.001 so, the probability that resistors R/2 and R has the samw probability of failure.

now in series at least one resistor is failing is equivalent to the system is failing.

So the probability is 2*(0.001) + (0.001)2 = 0.00201 .

(b) In parallel connection, the system fails when both the resisors fail, so the probability is (0.001)*(0.001) = 0.00001 .

(c) in series-parallel combination, with each resistor R , the system fails when one both of the two branches fail. Now one branch fails when at least one fails that is (0.00201)2 = 4.0401x10-6 .

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