Dear Allstats,
I have come across a problem on distribution which has
stymied me. I remember solving it some time back but
now I am getting a different answer. The problem goes
like this :
There are m+n tickets in an urn which are numbered 1,
2, 3,..., m+n. Suppose n tickets are drawn at random
from the urn. Show that the probability that x of the
tickets drawn will have numbers exceeding all numbers
on the tickets left in the urn is
(m + n - x - 1)C(m - 1) /(m + n)C(m).
Here is my approach.
Since there are m+n tickets in the urn and I have to
draw n tickets at random of which x tickets have
numbers exceeding all the numbers left, the x tickets
among the n drawn will have to be the largest numbers
from the lot. Therefore I consider the last x tickets
in the series {1, 2, 3, ..., m + n} already drawn. So
I have to calculate the probability of drawing n-x
tickets from a lot of m+n-x tickets, where the the
total number ways in which n tickets can be drawn is
of course (m+n)C(m).
Therefore the required probability is,
(m + n - x)C(m)/(m + n)C(m).
I would be much obliged if any one could point out to
me where I have made the mistake.
______________________
Indrajit SenGupta
Department Of Statistics
St. Xavier's College
Calcutta University
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