So I'm having problems with this one. It says:
We draw with replacement two balls from an urn containing k black balls and l white balls where $k\ne l$ (with replacement the question means: draw one ball put it back in the urn, draw another ball put it back in the urn. So the experiment we are working here consists in drawing these 2 balls and comparing them, if they have the same color we start over with another experiment). This process is repeated until, for the first time, we draw two balls with different colors. Calculate the probability that the last ball you draw from this pair is white.
And the possible answers are: a) l/(k+l), b) k/(k+l), c) 1/2, d) 3/4, e) l(1-l)/(l(1-l)+k(1-k))
Should I use Bayes? I'm having problems modeling this problem.
Best Answer
You can disregard all instances where both balls have the same color. Just condition on the event that you have drawn two different balls. The answer then is obvious.