<img src="asset:assets/questions/02a4075892b2a35e.jpg"><br/><br/>On a certain circular dartboard, the diameter of the circular bullseye is 4 inches and the diameter of the entire board is 20 inches. If a dart hits the board in a random location, what is the probability that it hits the bullseye target?
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✓ Correct answer: D. <tex>\displaystyle \frac{1}{25}</tex>While this problem asks about probability, it's essentially an area of a circle problem. The probability of hitting the bullseye is just the area of the bullseye divided by the area of the dartboard in total.<br/><br/>Since <tex>\displaystyle Area=\pi r^2</tex> your job becomes to find the radius of each circle. You're quoted the diameters, so to find the radius just divide the diameter by 2.<br/><br/>Bullseye: Diameter = 4 so Radius = 2. Area = <tex>\displaystyle \pi (2^2)=4\pi</tex><br/><br/>Dartboard: Diameter = 20 so Radius = 10. Area = <tex>\displaystyle \pi (10^2)=100\pi</tex><br/><br/>So the probability of hitting the bullseye is <tex>\displaystyle \frac{4\pi }{100\pi }</tex> which reduces to <tex>\displaystyle \frac{1}{25}</tex>.
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