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# Maria bought 4 black and a certain number of red and blue pencils at 1

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Manager
Joined: 16 Feb 2011
Posts: 179
Maria bought 4 black and a certain number of red and blue pencils at 1  [#permalink]

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24 Jul 2011, 00:36
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Question Stats:

80% (01:00) correct 20% (02:28) wrong based on 18 sessions

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Maria bought 4 black and a certain number of red and blue pencils at 15 cents each an carried them home in one bag. After Maria came home, she took out one pencil at random to write a note and then put the pencil back into the bag. Some time later, she needed to write another note and again took out a pencil from the bag. If the probability that Maria wrote both her notes in black is 1/36, how much did she spend on all pencils?
Manager
Status: Post application wait begins!
Joined: 15 Aug 2010
Posts: 138
Location: United States (CA)
Concentration: Strategy, Technology
GMAT 1: 720 Q50 V37
GPA: 3.82
WE: Engineering (Computer Software)
Re: Maria bought 4 black and a certain number of red and blue pencils at 1  [#permalink]

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24 Jul 2011, 00:44
1
Assume the total number of pencils in the bag to be x. We need to determine 0.15 * x to obtain the total cost.

P(drawing the first black pencil) = 4/x

P(drawing the second black pencil)=4/x (It's x and not x-1 because the problem says the first pencil was dropped back into the bag).

P(2 black pencils) = (4/x)^2

From the problem, p(2 black pencils) = 1/36.

Solving, we get x = 24, total cost of pencils = 3.60$_________________ Give me kudos if you like my post! Intern Joined: 14 Mar 2010 Posts: 15 Re: Maria bought 4 black and a certain number of red and blue pencils at 1 [#permalink] ### Show Tags 25 Jul 2011, 07:32 1 let x be the number of blue pencil and y be the number of red. We need to find the total number of pencil ( total cost = total number * 15 cents ) prob of picking a 2 blacks continuously = 4/(4+x+y) * 4/(4+x+y) = 1/36( from question ) solving : x+y = 20 . Hence total number = x+y +4 = 24 total cost = 24 * 15 = 3.6$
br,
Binu
Manager
Joined: 25 May 2011
Posts: 96
Re: Maria bought 4 black and a certain number of red and blue pencils at 1  [#permalink]

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23 Dec 2011, 05:46
X=the number of red and blue pencils

$$probability=\frac{4}{X+4}*\frac{4}{X+4}=\frac{1}{36}$$

So, X=20
Total pencils=24
Total cost$$=0.15*24=3.6$$ \$
Manager
Joined: 26 Apr 2011
Posts: 201
Re: Maria bought 4 black and a certain number of red and blue pencils at 1  [#permalink]

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27 Dec 2011, 05:13
well explained by shahideh. Now its clear to me. Thanks
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Re: Maria bought 4 black and a certain number of red and blue pencils at 1  [#permalink]

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14 Apr 2019, 16:14
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Re: Maria bought 4 black and a certain number of red and blue pencils at 1   [#permalink] 14 Apr 2019, 16:14
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