00:01
So we're looking at credit card fraud and checking transactions to see if they are fraudulent.
00:05
So a business has a fraud detection system offered to them.
00:10
It catches 99 % of fraudulent transactions.
00:14
So the probability of detection, given it is fraudulent, is 99%, or 0 .99.
00:21
The probability of detected, given it's not fraudulent, i'll put f -dash, is 2%.
00:32
So that's the information that we have been given here.
00:34
The probability of detection given a transaction is actually fraudulent and given it is not.
00:41
So in part 8, what would be the consequence of missing, of mistaking an honest transaction for a fraudulent one and vice versa? so if we have fraudulent given, detected given not fraudulent, the problem there is that somebody's transaction isn't going to go through and potentially they could get in some kind of trouble with their bank.
01:09
So they miss a sale and they annoy their customer.
01:18
What if they fail to detect a fraudulent transaction? so no detection given it was actually fraudulent.
01:27
So the problem there is they've let a fraudulent transaction go through and that can cause problems for a business when the credit card catches up to that fraudulent transaction, they often fine the business.
01:40
So they're going to lose out on that.
01:43
So fines, trouble with the credit card companies.
01:54
In extreme cases, if they do this enough, they might get their website banned from the use of credit cards, which is, of course, not good for a business.
02:05
In part b, so we've been given these conditional probabilities.
02:08
Probabilities.
02:08
Are these what the owners want to see? well, they're not the only ones that might be useful.
02:15
We might also want to see the probability that it was fraudulent, given it was picked up, or the probability that it is not fraudulent, given it was let through.
02:27
Those are more useful here.
02:32
And now we're actually going to look at those.
02:35
So let me make some space for part c.
02:47
There we go.
02:50
Part c.
02:51
Now we are told the prevalence of fraud is 1%.
02:55
Probability a transaction is fraudulent is 1%.
02:59
0 .01.
03:00
What is the probability of incorrectly labelling honest transactions as fraudulent? well, they've just asked us for probability of positive given it wasn't fraudulent.
03:13
That's 2%.
03:15
It's always 2%, but let's say that they probably want a bit more than that.
03:24
What is the probability that a transaction was not fraudulent, given it was picked up? so this is going to be, it was picked up, what's the probability? it is fraudulent.
03:39
Now when we want to flip conditional probability like this, we're going to be using bayes ' rule.
03:44
And there's a formula here.
03:46
The probability of b given a is equal to the probability of a given b multiplied by the probability of b divided by the probability of a...