3) Consider the above circuit which conducts current when a path exists from the

Question

3) Consider the above circuit which conducts current when a path exists from the input to output. Let Ri be the event that switch i (i = 1, 2, 3) is closed. Each switch operates independently and is closed with probability P(Ri) = pi , with p1 = 0.7, p2 = 0.3, and p3 = 0.4.

3a)Write in mathematical form, using the events Ri , the event that the system conducts current.

3b) Find the probability that the system conducts current.

3c) If we know the system is conducting current, what is the probability that switch 3 is closed?

Explanation / Answer

1. System conducts when swich 1 is closed and either switch 2 is closed or switch 3 is closed.

E = event that systemconducts.

Prob(E) = P(R1)*P(R2)+P(R1)*P(R3)

2. Prob(E) = 0.7*0.3+0.7*0.4

Prob(E) = 0.48

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