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A point with coordinates (x,y) is randomly selected such that 0 <= x <= 10 and 0 <= y <= 10 . What is the probability that the coordinates of the point will satisfy 2x + 4y >= 20? Express your answer as a common fraction.

 Mar 31, 2021
 #1
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Look  at  the  graph  here  :   https://www.desmos.com/calculator/2x44zxv4qs

 

The  first two constraints  form a 10 x 10  square.....the  area  =  100

 

The  unshaded area  in the constraint region   forms a  triangle   that  has  a base of 10  and a  height of 5

 

The  area of this triangle  = (1/2) (10)(5)   =  25

 

But....we  are  interested  in the  shaded area in the  constraint region....

 

This area =  100  - 25  =  75

 

The probability  that a  point falls into this   region  is   75 / 100  =   3 / 4

 

 

cool cool cool

 Mar 31, 2021
edited by CPhill  Mar 31, 2021
edited by CPhill  Mar 31, 2021
edited by CPhill  Mar 31, 2021

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