On a table there are two bags. The first contains one white marble. The second bag contains one red and one white marble. Blindfolded, Billy takes one marble out of the second bag and puts it in the first bag. He then takes off his blindfold and takes a marble out of bag one. It is a white marble.
What is the probability that the other marble in the first bag is also a white marble?

Dutch National Science Quiz 12/24/2004

(In reply to Solution by np_rt)

There's no need for the white marbles to be distinguishable in order to make the probability 2/3.  The presence of twice as many cases of choosing a white marble when both are now white, as when one is red and one is white is sufficient.

In terms of Baye's rule, if we take W as the event that a white ball was transferred and w as the event that you chose a white ball the unblindfolded time, we know p(W) is 1/2, and we get:

p(w) = p(W)*1 + (1-p(W))*1/2 = 3/4

p(W and w) = p(W)*1 = 1/2

p(W given w) = p(W and w) / p(w) = 1/2 / (3/4) = 4/6 = 2/3

 

Posted by Charlie on 2005-04-17 17:04:01