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# Marbles in a Bag - Riddle

Mon 8 Sep, 2008 12:33 am
A bag contains a single ball, which is known to be either white or black (with equal probability). A white ball is put in, the bag is shaken, and a ball is then randomly removed. The removed ball happens to be white. What is now the probability that the bag currently contains a white ball?

Provide a convincing argument that your solution is correct.
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Type: Question • Score: 0 • Views: 13,938 • Replies: 7

Robert Gentel

1
Mon 8 Sep, 2008 01:40 am
@Valedictum,
2/3

And why is this kind of probability so confusing to so many people?
0 Replies

pumpjockey

1
Mon 8 Sep, 2008 05:15 am
@Valedictum,
it's like SchrÃ¶dinger's Cat
100% until you look at it.
cicerone imposter

0
Mon 8 Sep, 2008 10:27 am
@pumpjockey,
pump is correct. LOL
0 Replies

Nick Ashley

3
Mon 8 Sep, 2008 10:43 am
Excluding Quantum Superposition, Robert is correct.

For the explanation, there are 3 possibilities:

1. The ball was black. A white was put in, and a white was taken out.
2. The ball was white. A white was put in, and the added one was taken out.
3. The ball was white. A white was put in, and the original one was taken out.

In 2 of the 3 possibilities, the original ball was white. 2/3.

In Quantum Theory, the original ball exists as both black and white at the same time. Only by observing it, does it choose one of the two states. However, once it is observed, the probability that it is white is still 2/3.
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dallasmath

1
Sat 10 Apr, 2010 08:38 pm
This reminds me of the Monty Hall problem:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

The answer is yes, you should switch doors as your probability of winning the car would be 2/3. Many people think it is 1/2 and that switching doors doesn't matter.
playnow254

1
Wed 1 Sep, 2010 08:40 pm
@dallasmath,
aha, but you have a 1/3 chance first then one is removed. unless you pick that door, you now have a 1/2 chance (and no I didn't take that from somewhere else
Now a boring solution

Assume
[1] [2] [3]
G C G
_______
Choose:1
Removed:3
Nothing better to switch because you have 50/50 either way.
_______
Choose2
Removed:1/3
Nothing better to switch because you have 50/50 either way.
_______
Choose:3
Removed:1
Nothing better to switch because you have 50/50 either way.
markr

1
Fri 12 Nov, 2010 11:38 pm
@playnow254,
Surely, you jest!

Choose:1, Removed: 3 -> you must switch to win
Choose:2, Removed:1/3 -> you must NOT switch to win
Choose:3, Removed:1 -> you must switch to win

You win two out of three times if you switch.
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