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 Answer
by K Sengupta)
Let us denote a white marble by H, and a res marble by E.
Before the operation:
First bag content: H
Second bag content: EH, or HE
After the first operation:
First bag content: HE, EH, or HH
Second bag content: H, or E
After the second operation, assuming wlog that the first marble in the first bag is removed, we have:
First bag content: H, E, or H
Thus, there are precisely three possible first bag contents after the second operation(regarding the order), preciserly two of which coresponds to the marble that is left in the bag being white.
Consequently, the required probability is 2/3.