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Checkerboard Chances

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 

Puzzle ID:#42219
Fun:*** (2.3)
Difficulty:*** (2.87)
Category:Probability
Submitted By:billy314*us****!!

 

 

 



Timothy has a checkerboard with ten rows and ten columns and a spinner with the numbers 1, 2, and 3. There is an equal chance of each number being spun. He first spins the spinner and moves a checker from the bottom-left corner up the number of spaces spun. He then spins the spinner again, this time moving the checker right the number of spaces spun. If he repeats this process twice more, what are the chances the checker will land on the same color as the square on which it started?


Hint

If in total, the checker moves up an even number of spaces and to the right an even number of spaces it will land on the same color it started on. If it moves up and to the right an odd number of spaces it will also land on the same color it started on.
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