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A point (x,y) with integer coordinates is randomly selected such that 0 ≤ x ≤ 8 and 0 ≤ y ≤ 4. What is the probability that x + y ≤ 4 ? Express your answer as a common fraction.

Please give a detailed solution with every step. 

 Jan 2, 2019
 #1
avatar+98005 
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We can do this with a graph

 

See here : https://www.desmos.com/calculator/2hkwxitnsh

 

The region formed by  0 ≤ x ≤ 8 and 0 ≤ y ≤ 4 is an  8 x 4 rectangle with an area of 32

 

The  inequality  x + y   ≤ 4     forms a triangular region within this rectangle ......the base and height of this  triangle  = 4....so its area =  (4 * 4)  / 2      =   16 / 2 = 8   

 

So.....the probability that a point falls within this triangle is 8 / 32   = 1 / 4

 

 

cool cool cool

 Jan 2, 2019

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