00:01
In this problem, we have given you purchase two external devices which is device 1 and then device 2, d1 and d2, to back up your stats project data.
00:14
Each device has 1 % chance of failure.
00:17
So here we do have the percentage chance of failure is 1 % in each cases.
00:23
Now we have to identify simple space in terms of failure or non -failure for the situation and define a random variable that reflects the number of copies of your data that you have available.
00:38
And then the sample space is both device not working and both device working and anything in between either one working or other is not working.
00:50
The random variable is the number of device working either represented by 0 or 1.
00:57
So as in programming as we use, 0.
01:00
Over 1 and then we have to find the probability function for this random variable then also ci that is cumulative probability function for this random variable so here let's solve this we can say defining the random variable as the number of working revise so we do have the sample space so simple space let's suppose here we do have represented by capital s so here we can say sample space would be 0 1 or 2 that means 1 is working no one is working no one is working and all are working.
01:34
So, here we can say this is a sample space represented with as here we can say for part a, we have sample space which is 0, 1 and 2.
01:46
And also we know that this is the binomial distribution.
01:49
So, for part b we can say this is the binomial distribution and probability of failing the device is 1 % that means this is 0 .01.
02:04
So probability of filling the device is 0 .01 or 1%.
02:08
So, this would be 0 .01.
02:13
Now, probability function for the working device would be, say, p probability function here, this would be 2cx, this would be 0 .01, reach to the power 2 minus x multiplied with 0 .0.
02:27
So, say, this would be 99, multiplied with x, for the values of x, which belongs, say this would be, which belongs from the set which is 0 1 and 2 and this would be 0 otherwise so probability of both device failing so if both device failing so this would be both device failing both device failing both device failing that means x is equals to 2 so this would be 2 2 2 2 2 1 and this would 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 probability of one device failing.
03:15
So here this would be equals to 2 multiplied widths.
03:18
So here we can say this would be here is two device and then one device is failing.
03:25
So here one device fail.
03:29
So this would be equals to 2 multiplied with 0 .01 multiplied with 0 .99.
03:37
So this is equals to 0 .098.
03:40
Now probability that none of the device fail.
03:43
Fails...