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?
(In reply to I think I'm beginning to understand what Ady's saying
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.