I'm just guessing here but wouldn't it depend on how they are picking?
For instance if one person picked first. Then the odds that the second person picks the same two digit number is 1/90. However what if they pick at the same time? Then this becomes a question of the same event occurring twice. I would look at it like a dice roll. What are the odds that both people roll a 6? Well that is (1/6)^2. What are the odds they both pick the same two digit number? (1/90)^2.
Might wait for another comment though, my probability engine isn't working well today.