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 namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability M that the new color will be one of theJaunecolors? Choose the most appropriate option.
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= 
<gadget id="calculator">4*10</gadget>
<output>40</output>
40   Jaune X= (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4= 
<gadget id="calculator">6*5 + 4</gadget>
<output>34</output>
34   Total combinations= 9 choose 3 = 84   Probability of Jaune MM = (40 + 34)/84 = 37/42.37/42
<result>B</result>
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 namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability M that the new color will be one of theJaunecolors?