So, now that we formally define what the principle behind equality of opportunity is, let's walk through the loan predict for example once more. In this scenario, we have two groups of people, blue and orange. And let's say, we're interested in making small loans subject to the following conditions. A successful loan makes $300 dollars. An unsuccessful loan costs $700 dollars. And everyone has a credit score between zero and 100. And let's first start by setting the threshold of a credit score of 50. Now, because the distributions of the two groups are slightly different, setting the threshold to a credit score of 50 gives us some decent results. For the Blue Group, a threshold of 50 leads to correct decisions, 76 percent of the time. For the Orange group, a threshold of 50 leads to correct decisions 87 percent of the time. So what this default threshold suggests is that it's better to be in the Orange group, than in the Blue group, meaning that there's room for improvement to be made here. Now, let's say you set your thresholds to maximize profit. If you look for pairs of thresholds that maximize total profit, maybe you'll see that the Blue group is held to a higher standard than the Orange one. And that's depicted in the slide here by the increase in dark grey shaded regions which represents those that were denied a loan, even though they would have paid it back. That could be a problem and one that suggests not just picking thresholds to make as much money as possible. Another technique would be to implement what's called a "group unaware" approach, which holds all groups to the same standard. So in this scenario, we'll use the same threshold, 55 for all groups. Is this really the right solution though? For one thing, if there are real differences between two groups, it might not be fair to ignore them. For example, women generally pay less for life insurance than men, since they tend to live longer. But there are other mathematical problems with group unaware approach, even if both groups are equally loan worthy. In the example above, the differences in score distributions means that the Orange group actually gets fewer loans when the bank looks for the most profitable group unaware threshold. But if we were to take the equality of opportunity approach, then in this example, among people who pay back a loan, Blue and Orange groups do equally well. This choice is almost as profitable as optimizing for maximum profits and about as many people get loans overall. Here the constraint is that of the people who can pay back a loan, the same fraction in each group should actually be granted a loan. Or using some of the jargon that was introduced in the earlier sections, the true positive rate is identical between the groups. So the takeaway to all of this, is that it's possible to find thresholds that meet any of these criteria. When you have control over your machine learning system, using these definitions can help clarify core issues. If your model isn't as effective for some group as others, it can cause problems for groups that have the most uncertainty. Restricting the equal opportunity thresholds transfers the burden of uncertainty away from the groups, and onto you, the creator of the model, doing to improvise the incentive to invest in the best classifiers.