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Probability of current flow through circuit

  1. Oct 12, 2009 #1
    The probability of the closing of the ith relay in the circuits shown is given by p_i. Let p_1 = 0.9, p_2 = 0.6, p_3 = 0.1, p_4 = 0.7, p_5 = 0.2. If all relays function independently. what is the probability that a current flows between A and B for the respective circuits?

    https://webwork.math.lsu.edu/webwork2_course_files/Math-3355-01-Fall2009/tmp/gif/HW4-prob1-ur_pb_4_14.gif


    3. The attempt at a solution

    I am working on the circuit in part B. I broke down the problem into 4 events in which the current could flow through the circuit. I labeled them A, B, C and D. I know that the problem is just P(AUBUCUD), but I do not know how to do a union for 4 events. Can someone please help?
     
    Last edited by a moderator: Apr 24, 2017
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  3. Oct 12, 2009 #2

    LCKurtz

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  4. Oct 12, 2009 #3
    - That is what I tried using actually, but I guess I'm not quite sure how to set up the formula once you get past 3 events.
     
  5. Oct 13, 2009 #4

    LCKurtz

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    Try just using a chain of conditional probabilities. Let:
    C = event that current flows
    s1 = event switch 1 is closed
    s2 = event switch 2 is closed etc.

    So you could start like this:

    P(C) = P(C|s1)P(s1) + P(C|s2)P(s2) = P(C|s1)(.9) + P(C|s2)(.6)

    Now to calculate P(C|s1) condition it on s3 and s4 and fill in what you know. Keep going like that.
     
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