# Professor's probability!

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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