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A point (x, y) is randomly chosen such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. What is the probability that y ≤ 2x?

 May 1, 2021
 #1
avatar+2127 
+3

We can solve this using geometry. :))

Drawing a 1 by 1 square, let one side be x, from 0 to 1. Let the other be y, from 0 to 1. 

Then shade in the area where y <= 2x, the area is 3/4. :))

 

=^._.^=

 May 1, 2021
 #2
avatar+121004 
+4

See  the  graph  here  :    https://www.desmos.com/calculator/1jam4kirxr

 

The  area of interest is a  trapezoid with a  height of 1  amd bases of 1  and 1/2   inside  a square  with an area of 1

 

The probabiluty is  just the  area of  the trapezoud =   (1/2) (1) (1 + 1/2)  = (1/2) (3/2)   =  3/4

 

Just as  catmg found   !!!!

 

 

 

 

cool cool cool

 May 1, 2021

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