Due if tori can enter her school by any one of the three doors and the school has two staircases to the second floor, in how many different ways can tori reach a room on the second floor? justify your answer by showing the sample space.

Well considering there are three doors and two staircases are at two doors, let's break this down. 

1 door could have a staircase and she could go through there.
1 door couldn't have a staircase and she could go through there.
1 door could have a staircase and she could go through there. 

She has a 2/3 chance of choosing a door with a staircase and a 1/3 chance of choosing the one without a staircase. 

It is more likely for her to go into a door with a staircase than without. 

But like I said we don't know where the rooms are so how are we supposed to know? We don't know how many rooms there are either. She could reach 20 classrooms before getting to a staircase or 10. It's a poorly worded question.

Hope this helps, sorry if it didn't!