Question
In Problem $62 \mathrm{a}$, find the conditional probability that relays 1 and 2 are both closed given that a current flows from $A$ to $B$.
Step 1
The probability that each relay is closed is 0.8, and the probability that each relay is open is 0.2. The relays operate independently. Let A be the event that a current flows from A to B, and let B be the event that relays 1 and 2 are both closed. We want to Show more…
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Key Concepts
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(a) In Problem $62 \mathrm{~b}$, find the probability that a current flows from $A$ to $B$ by conditioning on whether relay 1 closes. (b) Find the conditional probability that relay 3 is closed, given that a current flows from $A$ to $B$.
Conditional Probability And Independence
Self-Test Problems And Exercises
The probability of the closing of the ith relay in the circuits shown is given by pi. Let p1 = 0.6, p2 = 0.7, p3 = 0.5, p4 = 0.9, p5 = 0.1. If all relays function independently, what is the probability that a current flows between A and B for the respective circuits? (a) P = 0.0681 (b) P = .2842
The probability of the closing of the ith relay in the circuits shown is given by p_i. Let p_1 = 0.4, p_2 = 0.1, p_3 = 0.5, p_4 = 0.7, p_5 = 0.6. If all relays function independently, what is the probability that a current flows between A and B for the respective circuits? (a) P = .2256 (b) P = .3808
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