Two points are selected randomly on a line segment of length 20, one on each side of the midpoint of the line. That is, the two points X and Y are independent random variables such that X is uniformly distributed over (0, 10) and Y is uniformly distributed over (10, 20). Find the probability that the distance between the two points is greater than 8. Hint: Think of the pair (X, Y) as a point on the x-y plane (as in the Mr. Johnson and the newspaper problem) and identify the region where they're more than 8 apart.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Two points are selected randomly on a line segment of length 20, one on each side of the midpoint of the line. That is, the two points X and Y are independent
random variables such that X is uniformly distributed over (0, 10) and Y is uniformly distributed over (10, 20). Find the probability that the distance between the
two points is greater than 8. Hint: Think of the pair (X, Y) as a point on the x-y plane (as in the Mr. Johnson and the newspaper problem) and identify the region
where they're more than 8 apart..
Transcribed Image Text:Two points are selected randomly on a line segment of length 20, one on each side of the midpoint of the line. That is, the two points X and Y are independent random variables such that X is uniformly distributed over (0, 10) and Y is uniformly distributed over (10, 20). Find the probability that the distance between the two points is greater than 8. Hint: Think of the pair (X, Y) as a point on the x-y plane (as in the Mr. Johnson and the newspaper problem) and identify the region where they're more than 8 apart..
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