# robot climbing ladder with different probability to climb up at each bar

there is a ladder with 4 bars, a ground bar marked as bar 0. no bars beneath bar 0. no bar above bar 4. A robot starts climbing it up from bar 0. He will climb up or down the bars depending on the probability, at each bar, there is different probability to climb up as follows:

to climb up successfully:

from bar 0 to bar 1 : 1/3

bar 1 to bar 2: 1/4

bar 2 to bar 3: 1/5

bar 3 to bar 4: 1/6

if he fails, he will only drop down 1 bar. ex: from bar 3 to bar 2.

Question: what is the chance for robot climbing up to the 4th bar within N times?

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I don't see a question. – joriki Feb 21 '13 at 8:45
sorry about that, just edited. – cyanBigOcean Feb 21 '13 at 9:11
You haven't specified what happens when the robot fails to climb from bar $0$ to bar $1$. Does it stay at bar $0$ then? – joriki Feb 21 '13 at 9:30
yes, it does, it will just stay at bar 0 – cyanBigOcean Feb 21 '13 at 9:42
You should really grab an elementary text on finite Markov chains, this kind of question is quite standard... Norris comes to mind. – Did Feb 21 '13 at 10:29