In the x- y plane, there are 4 points (0,0), (0,4), (4,4), and (4,0).
In the x- y plane, there are 4 points (0,0), (0,4), (4,4), and (4,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
Answer/Solution
1/2
Steps/Work
If x+y<4, then y<-x+4.
The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.
The points below the line y=-x+4 satisfy x+y<4.
The area of this triangle is (1/2)(4)(4)=8
The area of the rectangle is 16.
P(x+y<4) = 8/16 = 1/2
The answer is A.
The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.
The points below the line y=-x+4 satisfy x+y<4.
The area of this triangle is (1/2)(4)(4)=8
The area of the rectangle is 16.
P(x+y<4) = 8/16 = 1/2
The answer is A.