A person works on the 7th floor of a 10 floor office building that has an unusua

Question

A person works on the 7th floor of a 10 floor office building that has an unusual elevator.

The elevator continuously moves between floors in sequence (1,2,3,4,5,... etc) and then

back down (10,9,8,7... etc) stopping only to pick up passengers. Assuming that the time it

spends exactly at each floor is negligible (ie, the elevator spends most of its time traveling

between floors), use probability to explain why this person frequently has to ride the

elevator up before going down to the first floor at the end of the work day.

Explanation / Answer

let time taken to cross each block by lift is x unit.

as for this person to come down, to ride the elevator down, he should wait for elevator b/w the time when it is going up and on 7th floor to when it comes back on 7th floor after reaching peak to coming back

hence total time so that he can catch elevator going down =6x (3 blocks up to 10th and then coming back 3 block down)

again for person to come down, to ride the elevator up,  he should wait for elevator b/w the time when it is going down and on 7th floor to when it comes back to 7th floor   after reaching 1st floor to coming back

hence total time so that he can catch elevator going up =12x (6 blocks bottom to 1st floor and then coming back 6 block up)

hence probabilty he catches elevator going up =12/18 =2/3

and probabilty he catches elevator going down =1/3

as probabilty of former is higher.,

this person frequently has to ride the

elevator up before going down to the first floor at the end of the work day.

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