Under different designs, what is the probability of hitting a white square on a

Question

Under different designs, what is the probability of hitting a white square on a square checkerboard? Start your constructions this way: 1 white square! Then, what is the next checkerboard? Four squares! What design follows? Continue designing checkerboards until you have one that is 10 by 10. As you build these checkerboards, calculate the probability of hitting a white square. When you are done, review your constructions and their corresponding probabilities, and make a generalization regarding the design (other than one white square!) that maximizes the required probability.  

Explanation / Answer

I take it for granted, you want the ratio of white squares tothe whole board. 'Hit' I take to mean throw a randomdart and record if it hits a white or black square (all mycheckerboards have been red and black).

1) 12 => 1 white square => 1 / 1 =100%

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