You are a newborn baby, whose parents are both eighteen years old and earn £15,000 a year in total. You live in a rough part of the city and your parents can just about scrape enough money together to feed themselves and you and keep your home. You have the potential to be a world-class scientist and solve the global warming crisis, however your parents will be unable to afford to send you to private school, you will need to rely on the government to help you reach your potential. Is the society fair or unfair? Write in three paragraphs.

This question reaches to the heart of a broader question about how societies are best organized. In particular, it raises issues about equality and, as the question indicates, fairness. Most would probably agree that it is unfair that a person with such talents will be unable to fulfill them because of the circumstances of their birth. After all, they had no control over their situation, and some would argue that even with a great deal of hard work, they still were unlikely to fulfill their potential. We might find unfairness and inequity in other aspects of the society described by the question as well. For example, why does this person have to attend private school in order to achieve their potential? If public school, accessible to all and funded by the state, is unable to allow students to maximize their talents, then clearly equality of opportunity does not exist in this society.
But at the same time, we have to acknowledge that the government described in the question provides support for students in this situation. The hypothetical student will, according to the question, "need to rely on the government" for help in reaching their potential. Some societies do not provide this basic support (though it is unclear what kind of help the government provides.) So this society seems to at least have a "safety net" to ensure that at least some talented people can fulfill their potential regardless of their socioeconomic circumstances. It also has to be acknowledged that some conservatives and libertarian-minded individuals would argue that government support for individuals like this is unfair inasmuch as it redistributes money from people who (they argue) earned it through their own labor to those who did not. So the concept of "fairness" cannot be taken for granted.
One measure of fairness that is at the heart of modern liberalism is that articulated by philosopher John Rawls, whose theory of justice essentially argued that a just society would be one that a person would want to be a part of without knowing what their social situation would be. In other words, the society would, as a fundamental principle, provide for its least fortunate members. This society seems to aspire toward this standard, as evidenced by the availability of help from the state, but it clearly falls short of it. In this hypothetical society, an individual's ability to fulfill their potential still depends on their circumstances rather than on their talents alone.
http://bostonreview.net/forum/economics-after-neoliberalism/corey-robin-uninstalling-hayek

https://plato.stanford.edu/entries/rawls/