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Topic: probability oddity, can someone explain?
Replies: 1   Last Post: Jun 22, 2011 5:55 AM

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Registered: 2/24/11
probability oddity, can someone explain?
Posted: Feb 24, 2011 6:49 PM
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I've been wondering about this since I got in an unresolved argument with my math teacher in school about 15 years ago, and I'm not sure what made me think about it again today, but I wonder if anyone here can give me a satisfying explanation please...

The question is: you have a bag that contains 10 marbles. 5 are white and 5 are black. If you pull out 3 marbles without replacement, what are the odds that all 3 will be white?

The textbook answer is 5/10 * 5/10 * 5/10 = 1/8

I get how that works for combinations/permutations.

However, that doesn't seem right to me, because I'm pulling these marbles WITHOUT REPLACEMENT.

It makes sense to me if I pull a marble out, it has a 5/10 chance of being white... if I throw it back into the bag and pull another marble, then it also has a 5/10 chance of being white again... but I'm not putting it back! I'm pulling these marbles WITHOUT REPLACEMENT.

So only the first one is a 5/10 chance of being white... When I go to pull the second marble, there are only 9 remaining in the bag, and my odds of the second one being white are 4/9 (not 5/10). Now that I've pulled 2 whites, there are 3 white + 5 black = 8 marbles remaining in the bag, so my odds of the third one being white are 3/8.

So my answer to this homework question was:
5/10 * 4/9 * 3/8

My math teacher said I was wrong and the answer is:
5/10 * 5/10 * 5/10

But why am I wrong?

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