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Coin on a Chessboard

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

 

Puzzle ID:#5328
Fun:*** (2.39)
Difficulty:*** (2.63)
Category:Probability
Submitted By:cathalmccabe***
Corrected By:cnmne

 

 

 



If a chessboard is the size of 80cm, and you throw a coin onto it of diameter 2cm. The centre of the coin falls somewhere within the 64 squares. What is the probability that it lands fully on a white square?


Answer

For the coin to fall within a white square, it (its centre) must fall into a smaller area inside a white square. This smaller area will also be a square with its length 2cm shorter than the 10cm white square. (If the coin falls at the very edge of the white square, its centre will be on the edge of this smaller white square; the border of this square will be 1cm away from the border of the larger square). So it must land within this area = 64 square cm.
The area of a white square is 100 square cm = 64/100, but only every 2nd square is white, so the answer = 32/100.

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