Max@Math Revolution wrote:In the x- y plane, there are 4 points (0,0), (0,4), (6,4), and (6,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 2/5

*Answer will be posted in 2 days.

I'm assuming x and y are the x- and y-coordinates of an ordered pair (x,y) lying inside the rectangle and selected at random.

The total area of the rectangle is 4x6=24 square units. Now imagine a line is drawn from (0,4) to (4,0). Every ordered pair lying below this line will fulfill the inequality x+y<4. This line forms a triangle when combined with the sides of our original rectangle. The triangle has area 1/2(4)^2 = 8. If we choose any ordered pair inside the rectangle at random, there is an 8/24 = 1/3 chance that such ordered pair will lie inside the triangle we created. Hence, the probability is 1/3.

As you can see from the diagram below, the correct answer is 1/3. Hence, B is our answer choice.