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Problem 4 Buffons needle problem 20 points graded on ac.pdf

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Problem 4 (Buffon's needle problem) (20 points, graded on accuracy) Figure 0.1. Needle intersecting the border of the ruled table A table is ruled with equidistant parallel lines with a distance D apart. A needle of length L is randomly thrown on the table. See Figure 0.1 , where X varies between 0 and D/2 and varies between 0 and /2. We assume that X and are uniformly distributed on those respective intervals. What is the probability that the needle will intersect one of the lines? (the other possibility being that the needle will be completely contained in the strip between the two lines). Break the problem into two cases: (1) Case 1: LD (10 points) (2) Case 2: L >D(10 points).

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Problem 4 (Buffon's needle problem) (20 points, graded on accuracy) Figure 0.1. Needle intersecting the border of the ruled table A table is ruled with equidistant parallel lines with a distance D apart. A needle of length L is randomly thrown on the table. See Figure 0.1 , where X varies between 0 and D/2 and varies between 0 and /2. We assume that X and are uniformly distributed on those respective intervals. What is the probability that the needle will intersect one of the lines? (the other possibility being that the needle will be completely contained in the strip between the two lines). Break the problem into two cases: (1) Case 1: LD (10 points) (2) Case 2: L >D(10 points)

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Problem 4 Buffons needle problem 20 points graded on ac.pdf

  • 1. Problem 4 (Buffon's needle problem) (20 points, graded on accuracy) Figure 0.1. Needle intersecting the border of the ruled table A table is ruled with equidistant parallel lines with a distance D apart. A needle of length L is randomly thrown on the table. See Figure 0.1 , where X varies between 0 and D/2 and varies between 0 and /2. We assume that X and are uniformly distributed on those respective intervals. What is the probability that the needle will intersect one of the lines? (the other possibility being that the needle will be completely contained in the strip between the two lines). Break the problem into two cases: (1) Case 1: LD (10 points) (2) Case 2: L >D(10 points)