. 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
Friday, December 28, 2007
QUESTION#13
Posted by Gaurav & Kunal at 10:49 PM
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4 Comments:
The answer is B) 37/42.
To find this out, we can consider the probability that it is not Jaune and then do 1 - that prob, to find the answer.
Now, if the new colour contains 1 Yellow it becomes Jaune Y and for 2 or more, it becomes Juane X.
Hence for it to not be Juane, we don't need any Yellow.
Number of ways to achieve that is (3 brown) or (1 brown + 2 red) or (2 brown + 1 red)
i.e. 3C3 + 3C1 * 2C2 + 3C2 * 2C1 = 1 + 3 + 6 = 10.
Total ways are 9C3 = 84
Hence For not Jaune Probability = 10/84.
So, for Jaune, Probability = 74/84 = 37/42 i.e. option (B).
Please can someone help me to find the flaw in my approach :
To have Jaune X the no. possible ways are 4C2*7C1. = 42.
To have Jaune Y the no. of possible ways are 4C1*5C2. = 40.
Total no. of possible ways of Jaune are : 42+40 = 82.
Total no. of possible combination of colors are 9C3 = 84.
The probability is = 82/84 = 41/42.
Can any one help me to find the flaw here.
Thanx & Regards,
-N.Solomon Harsha
Hi N.Solomon Harsha,
I think of a problem case, it is a silly mistake in your calculation.
First of all,
> To have Jaune X the no. possible ways are 4C2*7C1. = 42.
Well, to be Jaune X it should be,
4C2*5C1 + 4C3 = 30 + 4 =34.
Hence, total would be 40 + 34 = 74 ways.
And, Probability = 74 / 84 = 37/42.
Correct me if I am wrong in the explanation.
Hi Rushin
I have a question here ..
ways of selecting Juane is 74 ..this is fine
Now the number of ways of selecting Brun is 3C2 * 2C1 + 3C3 = 7
so adding up = 81 = number of ways of selecting a new colour wither Brun of Juane..
I think this way also, i should get 82 as total no of ways to select 3 object out of 9 = 9C3.
Can you please comment on this?
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