Give the exact results The following circuit operates if and...

Give the exact results The following circuit operates if and only if there is a path of functional devices from left to right. Assume devices fail independently and that the probability of failure of each device is as shown. What is the probability that the circuit operates F A 0.01 B 0.01 D 0.1 P1 C 0.1 E 0.1 P2 a) find the probability that P1 fail (a) 0.99801, b) 0.99; c) 0.997) b) find the probability that P2 fail ( a) 0.998; b) 0.99; c) 0.98) c) find the probability that the circuit fail ( a) 0.988 b) 0.899; c) 0.998)

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00:02 The circuit in the diagram shown works only if there's a path from the left side to the right side of it.

00:09 And the failures of the individual components, the probabilities of failure of the individual components, are shown for each component, so they're all .1.

00:19 And all devices are stated to fail independently of each other.

00:25 Now for part a, we're asked to find the probability that p1 fails.

00:28 So p1 is this subsystem here.

00:35 Now, p1 fails.

00:48 Actually, i wrote that wrong.

00:49 So the probability of p1 failing is equal to the probability that we have d fail.

01:02 So let's just call the component failing the letter that stands for the component.

01:08 So de -failing is d.

01:12 And either of a or b failing.

01:20 And since they are independent, this is equal to the probability of d failing, times the probability of a or b failing.

01:36 And the probability of a or b failing is equal to the probability of a failing plus the probability of b failing minus the probability of a and b failing.

01:52 And this is from probability theory.

02:08 The probability of a and b failing is the probability of a failing times the probability of b failing because they are independent.

02:32 Actually, they are not all 0 .1.

02:35 A and b have failure probabilities of .01.

02:38 It's always wrong about that...

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