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# A painter intends to mixed two jars of paint to create a new

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A painter intends to mixed two jars of paint to create a new [#permalink]  31 Aug 2012, 22:40
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A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 2 red and 2 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)

A. 1/5
B. 1/2
C. 2/3
D. 4/5
E. 6/5
[Reveal] Spoiler: OA
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Re: what is the probability that when mixed together, [#permalink]  31 Aug 2012, 23:14
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Let's start with the display, containing 3 red and 2 blue. If red is picked (60% chance of this happening), then the chance of picking blue from the other display is 50% (2/4). If blue is picked (40%), then the chance of picking red from the other display is also 2/4=50%. Since the chance of picking the right color will always be 50%, no matter, whether red or blue is picked first, the result is 50%.

0,6*0,5+0,4*0,5=0,5

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Re: what is the probability that when mixed together, [#permalink]  31 Aug 2012, 23:28
Why is the possibility of the mixing up of both colors (Red And Blue) from the same paint jar i.e from either the first jar or the second jar to produce purple color being neglected over here?. . Any clarity over this point is greatly appreciated.
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Re: what is the probability that when mixed together, [#permalink]  01 Sep 2012, 00:52
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The painter picks exactly one jar from Set A{R, R, B, B} and exactly one from Set B {R, R, R, B, B}.

The instructions simply state that he can't pick two from the same set.
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Re: A painter intends to mixed two jars of paint to create a new [#permalink]  01 Sep 2012, 04:59
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Vicky,

When the question ask about calculating the probability of some X, you don't need to calculate the probability of Y. However, you may use the Y to deduce X.

For example, what if the Question had asked "what is the probability of NOT creating purple color"
Here, you can calculate the probability of creating purple color. The probability of NOT creating purple will be (1 - P), where P is probability of creating purple color.
My point here is that if you consider only calculating what is being asked, it will help avoiding any confusion while making calculations.
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Re: A painter intends to mixed two jars of paint to create a new [#permalink]  25 Sep 2012, 06:14
Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B

FOR THE FIRST BUCKET ...

Red color - 2
Blue color - 2

FOR THE SECOND BUCKET

Red color - 3
Blue color -2

In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios :

Scenario I - He picks Red color from List A and Blue color from List B
Scenario II - He picks Blue color from List A and Red color from List B

Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5

Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ...

Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ...

We get 1/5 + 3/10 = 1/2 (B)
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Re: A painter intends to mixed two jars of paint to create a new [#permalink]  25 Sep 2012, 06:48
Probability of Picking Red Paint from Sample 1 = 2/4
Probability of Picking Blue Paint from Sample 1 = 2/4
Probability of Picking Red Paint from Sample 2 = 3/5
Probability of Picking Blue Paint from Sample 2 = 2/5

Now Probability of Purple(1 Red +1 Blue) -
Condition 1 - Choose red from 1 and blue from 2 = (2/4)*(2/5)
Condition 2 - Choose blue from 1 and red from 2 = (2/4)*(3/5)

Answer is sum of condition 1 and 2, hence 1/2, option B.
Re: A painter intends to mixed two jars of paint to create a new   [#permalink] 25 Sep 2012, 06:48
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# A painter intends to mixed two jars of paint to create a new

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