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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1432.0. "Urn probability" by ELIS::GARSON (V+F = E+2) Mon Apr 29 1991 10:53

An urn contains a number of balls each of which is either black, white or red.
It is given that the urn contains at least one black ball and at least one
white ball. k (> 2) balls are drawn from the urn with replacement. Given that
the probability that the balls drawn were all black or all white equals the
probability that the balls drawn were all red, find k and the number of balls
of each colour.
T.RTitleUserPersonal
Name
DateLines
1432.1marginal problemHERON::BUCHANANHoldfast is the only dog, my duck.Mon Apr 29 1991 11:406
	Ha!   A quaint setting.

	Now, what about the same problem, *without* replacement?

Cheers,
Andrew.
1432.2CADSYS::COOPERTopher CooperMon Apr 29 1991 15:534
    I have an interesting proof for my answer, but I'm afraid there isn't
    room in this note for it.

					Topher
1432.3is a countable infinity of answers enough?CSSE::NEILSENWally Neilsen-SteinhardtMon Apr 29 1991 16:103
>	Now, what about the same problem, *without* replacement?

k > 2, #black < k, #white < k, #red < k
1432.4solved for k =< 2HERON::BUCHANANHoldfast is the only dog, my duck.Mon Apr 29 1991 16:4734
1432.5k=3 has many solutionsCLT::TRACE::GILBERTOwnership ObligatesTue Apr 30 1991 13:2520
1432.6k=4CLT::TRACE::GILBERTOwnership ObligatesTue Apr 30 1991 13:433
And	b!/(b-4)! + w!/(w-4)! = r!/(r-4)!
has solutions:
	[7,7,8], and [132,190,200]
1432.7quick remarkHERON::BUCHANANHoldfast is the only dog, my duck.Wed May 01 1991 11:156
	In fact there's at least 1 solution for each k > 0.

	Let w = b = 2k-1, r = 2k.

Cheers,
Andrew.