The number of ways the 2 chosen students are from Grade 10, North \(= {}_{47} C_{2}=\frac{47!}{2!}\)

The number of ways the 2 chosen students are from Grade 10, South = \({}_{93} C_{2}=\frac{93!}{2!}\)

The number of ways the 2 chosen students are from Grade 11, North = \({}_{73} C_{2}=\frac{73!}{2!}\)

The number of ways the 2 chosen students are from Grade 11, South = \({}_{57} C_{2}=\frac{57!}{2!}\)

The total number of ways 2 students are chosen = \({}_{270} C_{2}=\frac{270!}{2!}\)

$$\therefore P(same\ grade\ and\ same\ school) \approx \frac{\frac{47!}{2!}+\frac{93!}{2!}+\frac{73!}{2!}+\frac{57!}{2!}}{\frac{270!}{2!}}$$