tomj@chinet.UUCP (Tom) (02/13/86)
This problem originally appeared (to the best of my knowledge) as one of
ten questions on Part II (of X) Actuarial Exams back when it was essay-
format rather than multiple-choice. The test was three hours long.
Question: Given a collection of w white balls and b black
balls drawn blindly from an urn, what is the
most probable (mode) number of changes of color?
(_e.g._ Given two white balls and one black
ball, the most probable number of changes of
color is 1:
001 -- one change
010 -- two changes
100 -- one change
P{1 change|2 white, 1 black} = 2/3
I have not yet solved this problem. Expanding the problem, given m objects
of type I, and n objects of type II, what is the probabilistic distribution
of the number of changes of type?
[This seems to have some cryptanalytic importance to me. Does it?]
_____
Tom Johnston ...ihnp4!chinet!tomj
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Disclaimer: I voted; but we were in Chicago, and you have to be dead to vote
there.