00:01
So in the following diagram, we have been given a circuit.
00:05
And we have been told that the following circuit operates if there is a path of devices that go from left to right.
00:14
And they've given a probability that each device functions, which is shown by the numbers on this.
00:19
And we've been given that the devices could fail independently.
00:23
So what is the probability that the circuit operates? so these three are in series.
00:28
Firstly, we have to note that.
00:29
And these three are in parallel, followed by this one being in series with the one that is parallel.
00:37
So we can calculate the independent probabilities independently because we've been told that the devices fail independently.
00:43
So let's say the probability that the series circuit on top works is 0 .9 cube, right? because the probability of them working is that.
00:58
All right.
00:59
So probability that the parallel works is essentially one minus the probability that all the three devices fail, right? three parallel, i'm just going to put it.
01:23
So three parallel fail, right? and this is one minus 1 .9, which is the probability of this one failing times.
01:38
1 minus 0 .95, which is the one below that failing, and 1 minus, so i'm just going to, i didn't realize that that is 0 .952, so you can just put square over here.
01:49
All right, and this is 0 .9975.
01:55
I'm writing all the numbers out because, you know, it's easy to get the final decimal more accurately when you do the calculation.
02:03
So now we have to calculate the probability that the three parallel and the one series after that works.
02:16
That is, i'm referring to the 0 .991.
02:20
That is right after the parallel circuits over here.
02:23
So the process and cell independent, we can just multiply the probabilities.
02:27
So that is 0 .99 -tripple -975 times 0 .99, which is 0 .9898.
02:35
So i'm just going to say this is 0 .997.
02:40
5 .9 .9...