00:01
So we know we have a poisson distribution and we know that the mean or the expected number, which is also the variance in this distribution, is that lambda, sorry, that doesn't look like a lambda, is equal to 0 .2 errors per page.
00:19
And we want to know in part a, what's the likelihood if x is the number of errors that there are two? and so we know our formula is to take the lambda to the k power times e to the negative lambda over k factorial.
00:36
And so in each case in this problem, it's going to be 0 .2 to the k, and then e to the negative 0 .2 and divided by whatever k factorial is.
00:46
So here we're going to end up having the point 2 to the second power times e to the negative point 2 divided by 2 factorial.
00:55
And when we get that calculation, that comes out to be .0164 to four decimal places.
01:02
Then we want to know what's the probability of having no errors, no air.
01:09
And so that's going to end up being that point two to the zero with power, e to the negative point two, and then we're going to have zero factorial.
01:19
And so we know that that is one and that is one.
01:24
So in essence, that's just going to come out to be the e to the negative point two.
01:30
Just one second.
01:34
And that comes out to be 0 .817.
01:39
Now, part c, we want to know what's the probability of having the number of errors being greater than or equal to three on that page.
01:47
And that's going to equal 1 minus the probability of having 0, 1, or 2 air.
01:55
And we already know this one and this one.
01:57
And let's find the probability.
01:59
So we know the probability of having zero error is 0 .0164.
02:05
We know the probability of having two airs is 0 .8187.
02:10
And let's find the probability of 1.
02:12
And the probability of 1 is putting 1 here and 1 here.
02:16
So that's going to end up being, let me quick go back and calculate that.
02:22
That's going to end up being 0 .164.
02:26
And so 1 minus that left parentheses .0164 plus .1637 plus .187 plus .817.
02:44
If i just type that in correctly, that should give me a small probability .0012.
02:50
We can also go through and use our poisson distribution, which the cumulative distribution.
02:58
And find if that, again, that value is 0 .2, and put in the x value of 2, and that will accumulate downward, and then do 1 minus that answer.
03:10
And i'm going to get a little bit different if i use the cumulative button.
03:14
If i use the cumulative button, i'm going to get an answer 0 .011, and that didn't allow any rounding error, which would be better naturally.
03:23
And then part d, we go, if we have a total of five pages, we want to know what's the likelihood that we have two airs, probability of two having no air.
03:38
Let me raise that.
03:42
No air in exactly two of those five pages, two of the five pages.
03:53
And so that's going to follow a binomial distribution.
03:55
And we have five pages, and we want two of them to have no airs.
03:59
And we know the probability of a no air is this .8187...