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A 2 by 2003 rectangle consists of unit squares as shown below. The middle unit square of each row is shaded. If a rectangle from the figure is chosen at random, what is the probability that the rectangle does not include a shaded square? Express your answer as a common fraction.

 Dec 23, 2018
 #1
avatar+3715 
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Just a few combinations would work...I'll try to create a solution...

 

1 step: Rectangle has 2 vertical and 2 horizontal lines.

 

You want to pick 2 vertical lines from the figure and two horizontal lines from the figure. 

The side lengths are 2004 * 3(increased by 1), so we have 2004C2 * 3C2, the choose function means combinations. 

 

Now, we have to get the non-shaded area, so is it 2*1002C2*3C2? Idk, can someone confirm

 

This is just complementary counting, so it is 1-X, the result. Is the answer \(\boxed{\frac{1002}{2003}}?\)

 

I'll try to confirm this later.

 Dec 23, 2018

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