Copied from www.greylabyrinth.com with a slight modification. I do think this is a good question that you have to think about before plunging into solving the equations.

I have 792 black marbles and 243 white marbles. I will draw one at random and discard it into a fiery pit. I will then keep drawing more random marbles and discarding them until one doesn't match the previous one. That marble will not be discarded, but put back in the bag. The marbles will be reshuffled and the process will start over.

Example:

I draw a black marble and discard it.

I draw another black marble and discard it.

I draw a white marble and shuffle it back into the bag.

I draw a black marble and discard it.

I draw a white marble and shuffle it back into the bag.

I draw a white marble and discard it.

I draw another white marble and discard it.

I draw another white marble and discard it.

I draw a black marble and shuffle it back into the bag.

After a little while, eventually only one marble is left. What is the probability of it being black?

I have 792 black marbles and 243 white marbles. I will draw one at random and discard it into a fiery pit. I will then keep drawing more random marbles and discarding them until one doesn't match the previous one. That marble will not be discarded, but put back in the bag. The marbles will be reshuffled and the process will start over.

Example:

I draw a black marble and discard it.

I draw another black marble and discard it.

I draw a white marble and shuffle it back into the bag.

I draw a black marble and discard it.

I draw a white marble and shuffle it back into the bag.

I draw a white marble and discard it.

I draw another white marble and discard it.

I draw another white marble and discard it.

I draw a black marble and shuffle it back into the bag.

After a little while, eventually only one marble is left. What is the probability of it being black?

**Bonus:**What if there were 28449 white and 184930 black?1 comment | Leave a comment