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In the xy-plane, a triangle ABC consists of 3 points A(0,0),

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by Max@Math Revolution » Mon May 02, 2016 10:42 pm
In the xy-plane, a triangle ABC consists of 3 points A(0,0), B(6,0), and C(0,12). If a point (x,y) is in the triangle ABC, what is the probability that y is smaller than x?

A. 1/2
B. 1/3
C. 1/4
D. 2/3
E. 3/4

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by Max@Math Revolution » Sat May 07, 2016 7:09 am
The probability of y<x is same as "the area of OBC/the area of OBA". Since the lower base=OB=6, we get a/12. Also, if we substitute this into 2x+y=12, we get 2a+12. From this we get a=4. Then, we obtain a/12=4/12=1/3. Hence, the correct answer is B.
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