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# A box contains 8 pieces each of milk chocolate, white

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A box contains 8 pieces each of milk chocolate, white [#permalink]  15 Apr 2013, 06:18
Dear All,

I know this is not a GMAT question but it is very similar. Could someone explain how to answer this question ?

I am with a group of five of my friends. A box contains 8 pieces each of milk chocolate, white chocolate, and dark chocolate. The box is passed around the six of us, with each person taking 4 pieces. Assume that each person chooses at random without replacement from the available pieces. I am the last person to whom the box is passed. Find the chance that I pick 4 dark chocolates.

Thank you very much in advance.

Warm regards,

Olivier
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Re: A box contains 8 pieces each of milk chocolate, white [#permalink]  15 Apr 2013, 08:20
Expert's post
Suto wrote:
Dear All,

I know this is not a GMAT question but it is very similar. Could someone explain how to answer this question ?

I am with a group of five of my friends. A box contains 8 pieces each of milk chocolate, white chocolate, and dark chocolate. The box is passed around the six of us, with each person taking 4 pieces. Assume that each person chooses at random without replacement from the available pieces. I am the last person to whom the box is passed. Find the chance that I pick 4 dark chocolates.

Thank you very much in advance.

Warm regards,

Olivier

Ok, let me give you some ideas. Perhaps you will be able to figure it out.

It doesn't matter whether I am the last person or the first. Since each person is an equal element, the probability that any one picks 4 dark chocolates is the same. Also the probability of picking 4 dark chocolates in the first pick is same as picking 4 dark chocolates in the last pick.

The logic behind it is a little un-intuitive but I have discussed it in detail in this post. Check it out:
http://www.veritasprep.com/blog/2012/10 ... ure-again/

Now we need to find the probability of picking 4 dark chocolates in the first pick.

Find the total number of ways in which you can pick 4 chocolates:
all 4 same type,
3 same type 1 different,
2 same 2 same,
2 same 2 different
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Re: A box contains 8 pieces each of milk chocolate, white [#permalink]  15 Apr 2013, 08:36
Hi VeritasPrepKarishma,

I read your article, it is very clear! But I wanna know if I have understood correctly
Because, as you said, "the probability of picking 4 dark chocolates in the first pick is same as picking 4 dark chocolates in the last pick" the answer should be
$$\frac{8}{24}*\frac{7}{23}*\frac{6}{22}*\frac{5}{21}$$

Is it right?
Thanks
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Re: A box contains 8 pieces each of milk chocolate, white [#permalink]  15 Apr 2013, 09:12
Thanks Karishma for making the probability simple.

The probability of picking 4 dark chocolates is 8/24*7/23*6/22*5/21.

Can you point to a sample question in which the probability would be different in each subsequent pick after the 1st pick?
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Re: A box contains 8 pieces each of milk chocolate, white [#permalink]  16 Apr 2013, 00:03
Thank you taking the time to explain everything.
Is the answer of 8/24*7/23*6/22*5/21 correct ?
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Re: A box contains 8 pieces each of milk chocolate, white [#permalink]  16 Apr 2013, 02:59
Expert's post
Suto wrote:
Thank you taking the time to explain everything.
Is the answer of 8/24*7/23*6/22*5/21 correct ?

Yes it is.
Probability of picking dark chocolate in the first pick = 8/24
Now you have only 7 dark chocolates and 23 total so probability of picking it again = 7/23 and so on...
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Re: A box contains 8 pieces each of milk chocolate, white [#permalink]  16 Apr 2013, 03:00
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Expert's post
nt2010 wrote:
Thanks Karishma for making the probability simple.

The probability of picking 4 dark chocolates is 8/24*7/23*6/22*5/21.

Can you point to a sample question in which the probability would be different in each subsequent pick after the 1st pick?

If the first picks have no conditions, all picks are the same.
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Re: A box contains 8 pieces each of milk chocolate, white [#permalink]  16 Apr 2013, 03:41
Dear Karishma,

Thank you for the explanation. Everything is clear
Re: A box contains 8 pieces each of milk chocolate, white   [#permalink] 16 Apr 2013, 03:41
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