Discrete Mathematics Level 3

The grade 12 class of École Sainte-Anne has 100 students and exactly 100 lockers available.

The lockers are stacked as indicated in the picture and the row is exactly 50 lockers wide. (50 x 2 =100)

Romeo and Juliette would like to have lockers that are adjacent but the teacher has decided to randomly assign the lockers.

What is the probability that their lockers will be adjacent?

If the probability can be expressed as \( \dfrac ab\) for coprime positive integers \(a\) and \(b\), what is \(a+b?\)

Note: We define adjacent as having a common edge.


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