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 byron123 September 4th, 2008 11:56 PM

An urn contains a azure balls and c carmine balls.. (Help)

Quote:
 An urn contains a azure balls and c carmine balls, where a.c is different 0 (zero). Balls are removed at random and discarded until the first time that a ball (B, say) is removed having a different colour from its predecessor. The ball B is now replaced and the procedure restarted. This process continues until the last ball is drawn from the urn. Show that this last ball is equally likely to be azure or carmine.
Can anyone help me out as to how to approach & solve this question? I guess something with induction but I could really use some help..

Thanks!

 RFurball September 5th, 2008 03:10 AM

Perhaps you could try a few examples

That's a good question and I don't know the exact approach but if I were to try to solve it I would run through a couple of examples on paper.

First I would go through all the combinations of 2 azure and 1 carmine balls and see how the probability works out.

Next I would go through all combinations of 3 and 2 balls or 3 and 1 ball.

From these examples you may be able to pick out the pattern for a and c balls.

 cknapp September 10th, 2008 09:39 AM

Re: An urn contains a azure balls and c carmine balls.. (Help)

Hmm... this is a tricky question, but some things to think about that *may* help:

What is the probabilty that your first azure ball happens on the k-th selection? First carmine ball?
Then you have (a+c)+1-k balls remaining: How many azure balls do you have? How many carmine? (I.e. what is the probability of selecting an a or a c?)

You have to do something inductive, I would assume.

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