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Maybe Im interpreting the question wrong but wouldnt it be 1/2. The elevator goes sequentially up and then down and then up again. If the elevator is going up this time then it will go down next time and vice-versa. The elevator only goes 2 ways. we dont know which way its going this time. The options for the next time the elevator hits floor 4 is it is going up or down. 2 options of which we dont have enough information to make a judgment which. Thus 1/2 probability that it will be going up next time it hits floor 4. Maybe I interpreted the question wrong though...
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