2 In a Year 8 internal examination in a large school the Geography marks, \(G\), and Mathematics marks, \(M\), had means and standard deviations as follows.
| Mean | Standard deviation |
| \(G\) | 36.42 | 6.87 |
| \(M\) | 42.65 | 10.25 |
Assuming that \(G\) and \(M\) have independent normal distributions, find the probability that a randomly chosen Geography candidate scores at least 10 marks more than a randomly chosen Mathematics candidate. Do not use a continuity correction.