Confusing Probability Problem

Revision en1, by TahsinEnesKuru, 2018-11-16 11:20:24

Hi everyone,

Today I came across with this problem :

There is a rabbit on the floor of the stairs. Stairs have 3 steps, Rabbit can jump 1 or 2 steps. What is the probability of going to third step from the floor without visiting second step ?

Yeah I know its very easy to see there are 3 possible ways to go to 3 from the floor :

floor -> 1 -> 2 -> 3
floor -> 1 -> 3 ( This is the case we want).
floor -> 2 -> 3

So the answer must be $\text{[math]}$ $\text{[math]}$ .

Ok everything seems right. But if we represent this problem as a graph , In first step we must choose between 1 or 2 so the probability to go 1 is equal to $\text{[math]}$ $\text{[math]}$ . In second step we must choose between 2 or 3 so the probability to go 3 is equal to $\text{[math]}$ $\text{[math]}$ . So the overall the probability is equal to $\text{[math]}$ $\text{[math]}$ . Second solution have some differences from the first solution but I couldn't figure out what it is.