It's time for the finals

Five students are taking a final exam consisting of only a single multiple choice problem with four options. The testing is done online and the students are finishing at different times in a random order. Due to an error in the software, each student (except the first) is able to see the answer submitted earlier by one other, randomly selected, student. Only one of the students has studied and is confident. He will always stick to his answer, but his probability of making the correct choice is actually only \(\frac34\). The remaining four are completely unprepared and will always copy.

What is the probability that the last person to finish gives the correct answer?

If the probability is in the form \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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