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Geometric Probability

In this type of problem, you will be given two figures, with one inside the other. You’ll then be asked what is the probability that a randomly selected point will be in the smaller figure. These problems are solved with the same principle we have been using:
 
Example

In the figure, the smaller square has sides of length 2 and the larger square has sides of length 4. If a point is chosen at random from the large square, what is the probability that it will be from the small square?

 

 
 
Solution

Applying the probability principle, we get

 


 





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