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In Problem 3 66a find the conditional probability that relays 1

In Problem 3.66a, find the conditional probability that relays 1 and 2 are both closed given that a current flows from A to B.

Problem 3.66

The probability of the closing of the ith relay in the circuits shown in Figure 3.4 is given by pi, 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?

Condition on whether relay 3 closes.

(a)

(b)

FIGURE 3.4: Circuits for Problem 3.66

Problem 3.66

The probability of the closing of the ith relay in the circuits shown in Figure 3.4 is given by pi, 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?

Condition on whether relay 3 closes.

(a)

(b)

FIGURE 3.4: Circuits for Problem 3.66

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