We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

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

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

9 Online Users