Tough Puzzles & Brain Teasers
Puzzles on logic and mathematics that will make you scratch your head.
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Kunal Gokhe
Mechanical
08 Feb 2019

# Bags of Marbles Puzzle

You have 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.

It is a white marble.

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

2mos ago

50%

Kunal Gokhe
Mechanical
2mos ago

@Ramani Aswath Good try sir but answer is 2/3.

2/3 (not 1/2)

You know that you do not have Bag B (two black marbles) so there are three possibilities

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.

Why not 1/2? You are selecting marbles, not bags.

2mos ago

@Kunal Gokhe , you are right. You are selecting marbles, not bags.

The second marble can be only white or black. So it is 1/2. Not 2/3.

2mos ago

You already have a bag and have already chosen a marble, which is white. The bag has to be white-white or white-black. So the only choices left are white if it is a white-white bag or black if it is a white-black bag.

So it is 50-50.

Kunal Gokhe
Mechanical
2mos ago

@Ramani Aswath yaa, sir i think you are right