SOLUTION: A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hitsthe dartboard at some point Q in the circle. What is the probability t
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Question 389392: A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hitsthe dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the circlethan the periphery?
Answer by gwendolyn(128) (Show Source): You can put this solution on YOUR website!
Let's assume that the point within the circle is chosen at random. Since the radius of the circle is 1, the point is closer to the center than the periphery if it falls within an inner circle with radius 1/2. To determine the probability that the point falls within this inner circle, we will compare the areas of the inner circle to the area of the entire circle. So, we use the Pr^2 (where P is pi) formula for area to compute the ratio of:
(area of inner circle of radius 1/2):(area of entire circle of radius 1)
The P's cancel out:
Doing the squares:
We ignore dividing by one, so the answer is:
1/4
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