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

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

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New post 24 Jul 2011, 00:36
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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?
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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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New post 24 Jul 2011, 00:44
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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$
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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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New post 25 Jul 2011, 07:32
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 $
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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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New post 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\(=0.15*24=3.6\) $
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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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New post 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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New post 25 Mar 2017, 01:41
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Re: Maria bought 4 black and a certain number of red and blue pencils at 1 &nbs [#permalink] 25 Mar 2017, 01:41
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