Find the probability that a point chosen at random in the figure lies in the shaded region.   http://www.flickr.com/photos/93084714@N07/8619998387/in/photostream

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violy | High School Teacher | (Level 1) Associate Educator

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First, take the area of the bigger circle which has a radius "r". 

So, area of the larger circle = pir^2. 

For teh area of the smaller circle, we replace the ="r" on the formula 

by r/2. 

Area of the smaller circle = pi(r/2)^2 = pir^2/4. 

For the area of the shaded region, we subtract the area of the bigger circle by the area of the smaller circle. 

Area of the shaded region will be: 

`pir^2 - (pir^2)/4 = (4pir^2 - pir^2)/4 = (3pir^2)/4`

FOr the probability that a point chosen lies on the shaded region will be calculate by dividing the area of the shaded region over area of the larger circle. 

`((3pir^2)/4)/(pir^2) = ((3pir^2)/4)*(1/(pir^2)) = 3/4.`

Therefore, the probability that a point chosen at random in the figure lies in the shaded region is 3/4 or 75%.

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