N rooms are there and they are numbered from 1 to N.
A person P is in charge of room allocation and allocates these rooms inthe following way:
K is a positive integer $\leq$ N. What is the reccurece relation for the probability of Kth room being filled up after the room allocation process has been stopped.
one example :
If initially 4 rooms are given [1,2,3,4].
First query : assume P selects (2,3)
Seconds query onwards can not be processed. because although 1,4 are vacant, these rooms are not consecutive.
how can we do this? :-/
i could only figure out that ,in your example (1,2,3,4)
for,1 to be filled,2 should be filled .
for 2 to be filled,1 or 3 should be filled.
for 3 to be filled,2 and 4 should be filled.
and for 4 to be filled,3 should be filled.
for corner rooms,the probability that they are filled is 1/nC2
for other rooms,the probabioty that they are filled is 2/nC2 (considering their adjacent rooms)
pls help further in solving and correct me :)
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