# Homework Help: Probability of current flow through circuit

1. Oct 12, 2009

### snoggerT

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
2. Oct 12, 2009

### LCKurtz

3. Oct 12, 2009

### snoggerT

- 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.

4. Oct 13, 2009

### LCKurtz

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.