+296 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.
+129852 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
