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

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Intern
Joined: 16 Nov 2012
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A box contains 8 pieces each of milk chocolate, white [#permalink]

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15 Apr 2013, 07:18
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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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Location: Pune, India
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Re: A box contains 8 pieces each of milk chocolate, white [#permalink]

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15 Apr 2013, 09:20
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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Karishma
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews VP Status: Far, far away! Joined: 02 Sep 2012 Posts: 1123 Location: Italy Concentration: Finance, Entrepreneurship GPA: 3.8 Followers: 176 Kudos [?]: 1861 [0], given: 219 Re: A box contains 8 pieces each of milk chocolate, white [#permalink] ### Show Tags 15 Apr 2013, 09:36 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 _________________ It is beyond a doubt that all our knowledge that begins with experience. Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b] Manager Status: Looking to improve Joined: 15 Jan 2013 Posts: 177 GMAT 1: 530 Q43 V20 GMAT 2: 560 Q42 V25 GMAT 3: 650 Q48 V31 Followers: 1 Kudos [?]: 57 [0], given: 65 Re: A box contains 8 pieces each of milk chocolate, white [#permalink] ### Show Tags 15 Apr 2013, 10:12 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? _________________ KUDOS is a way to say Thank You Intern Joined: 16 Nov 2012 Posts: 3 Followers: 0 Kudos [?]: 0 [0], given: 1 Re: A box contains 8 pieces each of milk chocolate, white [#permalink] ### Show Tags 16 Apr 2013, 01:03 Thank you taking the time to explain everything. Is the answer of 8/24*7/23*6/22*5/21 correct ? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6960 Location: Pune, India Followers: 2024 Kudos [?]: 12704 [0], given: 221 Re: A box contains 8 pieces each of milk chocolate, white [#permalink] ### Show Tags 16 Apr 2013, 03:59 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... _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6960
Location: Pune, India
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Re: A box contains 8 pieces each of milk chocolate, white [#permalink]

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16 Apr 2013, 04:00
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KUDOS
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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Karishma
Veritas Prep | GMAT Instructor
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Get started with Veritas Prep GMAT On Demand for \$199

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Intern
Joined: 16 Nov 2012
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Re: A box contains 8 pieces each of milk chocolate, white [#permalink]

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16 Apr 2013, 04:41
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, 04:41
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