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.
+128408 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
