# Thread: what is the probability

1. ## what is the probability

The vertices of a rectangle lie on the coordinate plane at the coordinates (1,1), (5,1), (1,7), and (5,7). If a point is randomly selected within the rectangle, what is the probability that the x-coordinate of the point is greater than the y coordinate?

2. Originally Posted by perash
The vertices of a rectangle lie on the coordinate plane at the coordinates (1,1), (5,1), (1,7), and (5,7). If a point is randomly selected within the rectangle, what is the probability that the x-coordinate of the point is greater than the y coordinate?
Draw a diagram. The area of the rectangle is 24 square units. The area of
the triangle cut off inside the square by the line x=y for which x>y is 8 square units.

Therefore the probability is the ratio of these areas = 8/24.

RonL

3. Originally Posted by perash
The vertices of a rectangle lie on the coordinate plane at the coordinates (1,1), (5,1), (1,7), and (5,7). If a point is randomly selected within the rectangle, what is the probability that the x-coordinate of the point is greater than the y coordinate?
I have nothing more to add to what Captain Black said except that you probably thought you had to derive an equation for the line and do some integration. Probability problems always seem tougher than they actually are. Simplify and win.