geometric probability We randomly place two points M, N on the segment [0,1]. (a) What is the probability that from point M is closer to N than to zero? (b) What is the probability that the midpoint of the segment belongs to the interval [0;0.25]?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 36E
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geometric probability

We randomly place two points M, N on the segment [0,1].
(a) What is the probability that from point M is closer to N than to zero?
(b) What is the probability that the midpoint of the segment belongs to the interval [0;0.25]?

Expert Solution
Step 1

it is given that we randomly place two points M, N on the segment [0,1].

let the coordinate of point M is (x,0) and coordinate of point N is (y,0).

we have to find out the followings:- 
(a) the probability that point M is closer to N than to zero?
(b) the probability that the midpoint of the segment MN belongs to the interval [0, 0.25]?

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