A point (x,y) is randomly selected such that 0 <= x <= 3 and 0 <= y <= 6. What is the probability that x + y <= 5? Express your answer as a common fraction.
+2401 If x = 0, the chance x+ y <=5 is 1/6
If x = 3, then chance x+ y <=5 = 2/3.
Average of 1/6 and 2/3 is 5/12.
I hope that's right. :))
=^._.^=
+128474 Look at the graph here : https://www.desmos.com/calculator/e3xiqeprcw
The total area of the region = 3 * 6 = 18
The graph of the inequality x + y ≤ 5 forms a trapezoid with bases of 5 and 2 and a height of 3
The area of this trapezoid = (1/2) (3) ( 5 + 2) = 21/2 = 10.5
So.....the probability that a point falls into the trapezoid = 10.5 / 18 = 7/12
