Bags of Marbles - Puzzle

There are three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble. 

You pick a random bag and take out one marble, which is white. 

What is the probability that the remaining marble from the same bag is also white?

Here is the solution! 

Bags of Marbles Puzzle - Solution

What is the puzzle?

Well, the probability that the second marble is also white should be 1/2 not 2/3 as most of answers to this puzzle claims!

There is no way that you have picked up the bag B having 2 black marbles since the first marble you have drawn is white. Hence, you must have picked up Bag A or C.

Claim :  

You chose Bag A, first white marble. The other marble will be white

You chose Bag A, second white marble. The other marble will be white

You chose Bag C, the white marble. The other marble will be black

So 2 out of 3 possibilities are white.


Hence, 2/3 is the probability of the second ball is also white.


Correct Approach :

The probability of the particular bag being picked randomly is 1/3 initially. Once the bag picked and since the marble drawn from it is white, the bag must be either A (2 whites) or C (1 white, 1 black).

The probability that the bag you picked is A (or C) must be 1/2 and hence the probability that second marble is also white (or not white) has to be also 1/2.