Possibility Graph

Question

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

Hint: A graph is very helpful

Answer 1

P = (area of triangle) / (area of rectangle)

P = (1/2)(4)(4) / ((8)(4))

P = 1/4

Answer 2

Rectangle 8 by 4.... length is x=[0,8] and height h=[0,4]

x+y <= 4 ---> y <= 4 - x

The critical points are (0,4) , (1, 3), (2,2) (3,1) (4,0)

The right triangle formed is x=4 by y=4 which has area (1/2)(4)(4) = 8

the area of the ENTIRE rectangle is (8)(4) = 32

So the probability is 8/32 = 1/4