Professor's probability!

Discrete Mathematics Level 4

An absent minded professor lost his latest set of question papers. In a panic, he decided to give his students marks chosen from a uniform distribution of the reals from 0 to 100.

But there is a problem. Two of the students in his class are identical twins, who study together and so get the similar marks. If their marks differ by more than \(\large 20\), they will suspect that something is wrong.

The probability that the professor does not attract suspicion can be expressed in the form \(\large \frac{a}{b}\), where \(\large a\) and \(\large b\) are positive coprime integers, determine the value of \(\large a+b\).

Details and Assumptions
The marks need not be integers, they are simply real numbers. The maximum marks in the test were \(\large 100\), and minimum \(\large 0\).


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