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Suppose you toss a dart at a circular target of radius 10 inches. Given that the dart lands in the upper half of the target, find the probability that a) its distance from the center is greater than 5 inches. b) it lands within 5 inches of the point (0,5). Solution The region that consists of the possible places that the dart can land without going more than 5 inches away from the center is a semicircle of radius 5. The area of this is r2/2 = 25/2 in2. The area of the entire potential area that the dart can land is r2/2 = 50 in2. The area that has a distance from the center that is greater than 5 inches is then 50 in2 - 25/2 in2 = 75/2 in2. Hence, the probability is (75/2 in2)/(50 in2) = 3/4. For the second question, the possible region that the dart can land in is a circle of radius 5, so it has area 25 in2. Since the total area that the dart can land in we found as 50 in2, the probability that the dart lands within this region is (25 in2)/(50 in2) = 1/2..

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Suppose you toss a dart at a circular target of radius 10 inches. Given that the dart lands in the upper half of the target, find the probability that a) its distance from the center is greater than 5 inches. b) it lands within 5 inches of the point (0,5). Solution The region that consists of the possible places that the dart can land without going more than 5 inches away from the center is a semicircle of radius 5. The area of this is r2/2 = 25/2 in2. The area of the entire potential area that the dart can land is r2/2 = 50 in2. The area that has a distance from the center that is greater than 5 inches is then 50 in2 - 25/2 in2 = 75/2 in2. Hence, the probability is (75/2 in2)/(50 in2) = 3/4. For the second question, the possible region that the dart can land in is a circle of radius 5, so it has area 25 in2. Since the total area that the dart can land in we found as 50 in2, the probability that the dart lands within this region is (25 in2)/(50 in2) = 1/2..

- 1. Suppose you toss a dart at a circular target of radius 10 inches. Given that the dart lands in the upper half of the target, find the probability that a) its distance from the center is greater than 5 inches. b) it lands within 5 inches of the point (0,5). Solution The region that consists of the possible places that the dart can land without going more than 5 inches away from the center is a semicircle of radius 5. The area of this is r2/2 = 25/2 in2. The area of the entire potential area that the dart can land is r2/2 = 50 in2. The area that has a distance from the center that is greater than 5 inches is then 50 in2 - 25/2 in2 = 75/2 in2. Hence, the probability is (75/2 in2)/(50 in2) = 3/4. For the second question, the possible region that the dart can land in is a circle of radius 5, so it has area 25 in2. Since the total area that the dart can land in we found as 50 in2, the probability that the dart lands within this region is (25 in2)/(50 in2) = 1/2.