Author |
Topic: More Balls and Urns (Read 1027 times) |
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender: 
Posts: 4489
|
 |
More Balls and Urns
« on: Dec 23rd, 2008, 7:57am » |
 Quote  Modify
|
An urn contains w > 2 white balls and b black balls. If 3 balls are wihdrawn from the urn the probability that they are all white is p. Having another white ball in the urn would increase this probability to 4p/3.
What is the maximum possible value of b?
|
|
 IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: More Balls and Urns
« Reply #1 on: Dec 23rd, 2008, 8:13am » |
Quote Modify
|
p = w/(w+b)(w-1)/(w+b-1)(w-2)/(w+b-2)
4/3p =(w+1)/(w+b+1)(w)/(w+b)(w-1)/(w+b-1)
divide the two to get
4/3 = (w+1)/(w+b+1) / ((w-2)/(w+b-2))
4(w+b+1)(w-2) - 3 (w+1)(w+b-2) = 0
b = (w-2)(w+1) / (11-w)
b = 88 is the maximum (for w=10).
|
| « Last Edit: Dec 23rd, 2008, 8:14am by towr » |
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
SMQ
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 2084
|
|
Re: More Balls and Urns
« Reply #2 on: Dec 23rd, 2008, 8:20am » |
Quote Modify
|
Darn, towr beat me to it -- same calculation. The other possible values are: w = 5, b = 3; w = 7, b = 10; w = 8, b = 18; and w = 9, b = 35.
--SMQ
|
|
IP Logged |
--SMQ
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print