The probability of the closing of the ith relay in the

Chapter 3, Problem 66P

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QUESTION:

The probability of the closing of the ith relay in the circuits shown in Figure 3.4 is given by \(p_i\), i = 1, 2, 3, 4, 5. If all relays function independently, what is the probability that a current flows between A and B for the respective circuits?

Hint for B: conditions on whether relay 2 closes

             

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QUESTION:

The probability of the closing of the ith relay in the circuits shown in Figure 3.4 is given by \(p_i\), i = 1, 2, 3, 4, 5. If all relays function independently, what is the probability that a current flows between A and B for the respective circuits?

Hint for B: conditions on whether relay 2 closes

             

ANSWER:

Step 1 of 3

(a)

We are asked to find the probability that a current flows between \(A\) and \(B\) for the respective circuits.

The probability of the closing of the ith relay in the circuits shown in the figure is given by \(p_{i}=1,2,3,4,5\).

Given all the relays function independently.

Let \(E\) be the event that current flows from \(A\) to \(B\). Then

                                               

 

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