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Simpler probability problem? (Posted on 2015-08-11) Difficulty: 1 of 5
An urn contains 5 black and 20 white marbles. They are to be drawn one at a time until all of one color has been exhausted.

What is the probability that the color of the first draw correctly predicts the first color exhausted?

No Solution Yet Submitted by Jer    
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Hints/Tips re: I think I'm beginning to understand what Ady's saying | Comment 13 of 14 |
(In reply to I think I'm beginning to understand what Ady's saying by Charlie)

Neither you nor I provide the answer to the question as it asked by Jer.

Your proof and simulation (both are errorless, taking 70 as a fair approximation of 66.666...) prove the following:

1, we know a priori that there is 1/3 prob of matching colors between the 1st drawn and the "exhausting" marble.

2. we know a priori that there is 2/3 prob of opposite colors between the 1st drawn and the "exhausting" marble.

3. we know a priori that there is 4/5 prob. of the  black marble being  the "exhausting" marble

SAFE BETS (made a priori, before drawing):

a. black will terminate the process     4/5

b. the color , other than the 1st drawn will terminate
the process     2/3

SAFE BETS (made a posteriori, after drawing one marble):

a. black will terminate the process   
  odds dependant on 1st color: 20/24 or 19/24

b.   assuming an a priori bet exists:

if white was drawn, ask to double your previous bet: if  blackbeg to surrender by paying less.

What prob... etc (jer' question) rests ambiguous.

The numbers of marbles created a funny situation, the 1/3 being composed of 2 equal parts.   Try (25,1),(17,7) and (13,13 )

IMHO only in the 1st of my examples Jer's question merits an unambiguous, coherent answer.

Ch, if you disagree, please specify where. 



  Posted by Ady TZIDON on 2015-08-13 01:03:53
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