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14 May 2021, 02:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
62% (03:11) correct
38%
(03:18)
wrong
based on 173
sessions
History
Date
Time
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Not Attempted Yet
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
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
22 May 2021, 04:00
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Bookmarks
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.
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.
General Discussion
14 May 2021, 02:42
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As Jaune colour will be created as long as at least 1 of the 3 jars is yellow. Best way to solve is to find the possibility of getting zero yellow jars into in the mixture and subtracting that from 1.
1 - (5/9 * 4/8 * 3/7)
= 1 - (5/42)
= 37/42
Answer B
1 - (5/9 * 4/8 * 3/7)
= 1 - (5/42)
= 37/42
Answer B
