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 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.