00:01
We are going to have to apply the law of total probability to this.
00:04
Before we do that, we must calculate the given components.
00:07
That is, what is the probability of a, that there is no error, given that we take path 1? well, it's going to be the probability that we take that path 1 of root 1 or root 2 minus the intersection of both.
00:23
And that's going to get us about 2 .4%.
00:28
Now for the probability of a given b complement that we take the other path.
00:36
This is going to be a 2 % chance for server free failing plus a 0 .03 % chance of server 4 failing minus the probability that they both fail.
00:54
And that gets us 0 .02294.
00:59
And now we can find out what the probability of no error is, which is going to be 1 minus the probability of a given b times a probability of b plus probability of a given b complement that we take the other path times the probability that we take the other path.
01:31
And this is going to be that number right there, 0 .02485, times the probability of b, which, we got as 30%.
01:53
And then we are going to add that to the other probability of 0 .02994 times the probability of b complement, which is going to be 70%...