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Billy's bag (Posted on 2005-04-17) Difficulty: 2 of 5
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

See The Solution Submitted by Hugo    
Rating: 3.0000 (2 votes)

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more manually | Comment 6 of 18 |

First bag's marble = w1. Second bag's marbles = w2 and r.

Once transferred a marble from the second bag, the first bag could only have (w1, w2) or (w1, r).

If we take randomly a marble out of the bag, the probability we have taken w1, while on the bag rests w2 is 1/4; for (w2, w1) is 1/4; and the same for (w1, r) and (r, w1).

But if we impose that the marble we have picked out of the bag is not randomly, but a white one, the last of these possibilities (= r, w1) is excluded. In our hands we have probably w1 (p=2/3) or perhaps w2 (p=1/3), and in the bag lays w2 or w1 or r, each one with equal probability = 1/3.

Then, the probability that in the bag there is a white (w1 or w2)marble is 2/3.

These "easy" problems are far from being easy for people who are not used to (include mayself). 

Edited on April 17, 2005, 9:58 pm

Edited on April 17, 2005, 10:05 pm

Edited on April 17, 2005, 10:08 pm
  Posted by armando on 2005-04-17 21:56:02

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