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Kurt, a French painter, has 9 jars of paint: 4 jars of yello

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Kurt, a French painter, has 9 jars of paint: 4 jars of yello [#permalink] New post 04 Aug 2008, 09:36
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Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:

The paint will be named "Brun Y" if it contains 2 jars of brown paint and no yellow.
The paint will be named "Brun X" if the paint contains 3 jars of brown paint.
The paint will be named "Jaune X" if the paint contains at least 2 jars of yellow.
The paint will be named "Jaune Y" if the paint contains exactly 1 jar of yellow.

What is the probability that the new color will be one of the "Jaune" colors?

A. 5/42
B. 37/42
C. 1/21
D. 4/9
E. 5/9
[Reveal] Spoiler: OA
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Re: PS New Paint [#permalink] New post 04 Aug 2008, 10:30
durgesh79 wrote:
Kurt, a painter, has 9 jars of paint:
4 are yellow
2 are red
rest are brown
Kurt will combine 3 jars of paint into a new container to make a new color, which he will name accordingly to the following conditions:

Brun Y if the paint contains 2 jars of brown paint and no yellow
Brun X if the paint contains 3 jars of brown paint
Jaune X if the paint contains at least 2 jars of yellow
Jaune Y if the paint contains exactly 1 jar of yellow

What is the probability that the new color will be Jaune

a) 5/42
b) 37/42
c) 1/21
d) 4/9
e) 5/9


I get B.

Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40
Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34
Total combinations = 9 choose 3 = 84

Probability of Jaune = (40 + 34)/84 = 37/42
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Re: PS New Paint [#permalink] New post 02 Feb 2011, 06:32
One comment of that:
In the question it states: he will use the collors to make a new color.

But when you mix 3 yellow colors, can that be counted as a new color?
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Re: PS New Paint [#permalink] New post 02 Feb 2011, 07:15
Expert's post
craky wrote:
One comment of that:
In the question it states: he will use the collors to make a new color.

But when you mix 3 yellow colors, can that be counted as a new color?


Well, as OA is B then apparently - yes we can consider the mixture of 3 yellow jars as a new color. Also we are told that we get Jaune X if the paint contains at least 2 jars of yellow, so 3 jars of yellow paint also give Juan X. Though I agree with you that the question is a bit ambiguous (and not only about the issue discussed).

Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:

The paint will be named "Brun Y" if it contains 2 jars of brown paint and no yellow.
The paint will be named "Brun X" if the paint contains 3 jars of brown paint.
The paint will be named "Jaune X" if the paint contains at least 2 jars of yellow.
The paint will be named "Jaune Y" if the paint contains exactly 1 jar of yellow.

What is the probability that the new color will be one of the "Jaune" colors?

A. 5/42
B. 37/42
C. 1/21
D. 4/9
E. 5/9

Basically we are told that we get Jaune in case a container has 1 jar of yellow (Jaune Y), 2 jars of yellow (Jaune X), or all 3 jars of yellow (Jaune X).

So we can calculate the probability that the container does not have yellow paint at all and subtract it from 1: P(yellow>0)=1-P(zero \ yellow)=1-\frac{C^3_5}{C^3_9}=\frac{37}{42}, where C^3_5 is the ways we can choose ANY 3 jars out of 2 red+3 brown=5 jars (so not to have yellow) and C^3_9 is total ways to pick 3 jars out of 9.

Answer: B.
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Re: PS New Paint [#permalink] New post 02 Feb 2011, 09:40
B. using the long method of (4c1 * 5c2 + 4c2 * 5c1 + 4c3)/9c3 = 37/42
Re: PS New Paint   [#permalink] 02 Feb 2011, 09:40
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Kurt, a French painter, has 9 jars of paint: 4 jars of yello

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