GEOMETRIC PROBABILITY Clements MA 11713 Problem David shoots

GEOMETRIC PROBABILITY Clements MAΘ 11/7/13

Problem David shoots a target with bow and arrow. If his shot hits a random spot on the circular target of radius 5, what is the probability that its within 2 of the center? If we put two points on a circle, what’s the probability that they’re within 50 degrees of each other? (Out of 360 degrees)

Segments If we pick a random point A on the segment connecting (0, 2) and (2, 2), and a random point B on the segment (0, 0) and (2, 0). What’s the probability that A & B are within 2 of each other? If we randomly put points A & B on a segment of length 1, what’re the chances that they are within 0. 5 of each other?

Linear If Carl guesses a real number between 0 and 10, and Shomik tries to guess his number, what’s the probability that Shomik will get within 1 of Carl’s number? If the show begins between 3: 30 and 3: 40, and you randomly decide to get there sometime between 3: 30 and 3: 40, what are the chances you’ll get there before it starts?

Harder Problems Randomly pick a point P in square ABCD. What is the probability that triangle ABP is acute? Three points A, B, C are placed at random on a circle of radius 1. What is the probability for triangle ABC to be acute?

Review Two friends who take metro to their jobs from the same station arrive to the station uniformly randomly between 7 and 7: 20 in the morning. They are willing to wait for one another for 5 minutes, after which they take a train whether together or alone. What is the probability of their meeting at the station? Draw the diagram!