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Geometry Level 3

A point ( X , Y ) \displaystyle (X,Y) is randomly picked up inside a rectangle with vertices ( 0 , 0 ) ( 4 , 0 ) ( 4 , 1 ) ( 0 , 1 ) \displaystyle (0,0) (4,0) (4,1) (0,1) .

If the probability that X < Y \displaystyle X<Y can be stated in the form of a b \dfrac {a}{b} where a a and b b are coprime integers, then find the value of a + b a+b .


The answer is 9.

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Anik Mandal by Anik Mandal , 21, India

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3 solutions

Aaaaa Bbbbb
Mar 3, 2015

P = ( A B E ) ( A B C D ) = 1 8 = a b P=\frac{(ABE)}{(ABCD)}=\frac{1}{8}=\frac{a}{b} a + b = 9 a+b=\boxed{9}

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Zeeshan Ali
Apr 8, 2015

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Noel Lo
Mar 11, 2015

(1/2) * 1 * 1 / (4*1) = 1/8 where a=1 and b=8 so a+b = 9.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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