Monday, 23 March 2009

An Improved Solution to the Probability Problem

My last blog gave a labored explanation of why given R red balls and W white balls in a bowl, if they are removed one at a time randomly until one color has been totally removed, what is the probability that White will be exhausted first.

Joshua Zucker gave much more elegant expalantion for the reason the probability of white being exhausted first is red/(red + white)

His solution, in my words.. forget everything except the last ball in the bowl... whatever color it is is Not the color that was exhausted. So All we have to do to know the probability that White is exhausted, is find the probability that the last ball drawn if we emptied the bowl would be red. But if we look at all the possible orders of drawing all the balls, 4/7 of the first balls drawn are red, 4/7 of the second balls drawn are red..and the same continues all the way to the end; 4/7 of the final balls drawn will be red, meaning that in 4/7 of the trials, the white balls were exhausted first.

Now I'm thinking about the case of three colors, red, white and blue. I haven't started, so if you have an easy explanation, lay it on me.... otherwise, more later.

-------------- edited afterward...
ask and you shall receive... Joshua does what he does best, thinking and explaining his thoughts on the fly... see the comment and learn ....
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