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

Expert Answers
violy | Certified Educator

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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