00:01
On average, one person in a thousand makes a numerical error in their income tax return.
00:07
So per person, probability is 1 over 1 ,000, which is 0 .0 .1.
00:16
Okay, and we're looking at 10 ,000, so n equals 10 ,000.
00:21
We want to work out the mean and variance.
00:24
We also want to work out probability that 6, 7 or 8 contain an error.
00:28
So this is a binomial problem.
00:30
We have a series of independent trials, the random sample.
00:34
Each one has the same two possible outcomes, error or not.
00:40
So for the first part, we need to use the binomial formula, which is the probability of exactly x successes, which here means making an error, is equal to n choose x, p to be x, 1 minus p to the x, so let's start with six.
01:04
We're also going to find seven and eight, and we're going to add them all together.
01:13
So this term here is for how many different ways there are of putting the trials in order.
01:18
And it's a combinations thing with this formula.
01:26
So we have 10 ,000 choose six, which i'll find.
01:32
These may be some very, very large numbers here.
01:36
So it might be better to just, yeah.
01:38
Huge number, we'll just use this.
01:44
Govies out.
01:50
Next term is for the successes.
01:53
So that's the probability 0 .01.
02:01
To the power of the number of people who did make an error.
02:06
Like so.
02:07
And we have the failures.
02:09
So these are all the ones who didn't make errors.
02:16
So we have the probability of not making an error.
02:22
It's the power of how many times it happened.
02:23
So that would be 9 ,994, 9193, 999992.
02:34
And then when we've got these, we're going to add them up.
02:37
So let's do that...