Point $(x,y)$ is randomly picked from the rectangular region with vertices at $(0,0),(2009,0),(2009,2010),$ and $(0,2010)$. What is the probability that $x > 7y$? Express your answer as a common fraction.

Accepted Solution

Answer: Probability that [tex]x>7y[/tex] is [tex]\frac{287}{4020}[/tex]Step-by-step explanation:Since we have given that [tex]x>7y[/tex]And the coordinates are as follows:(0,0),(2009,0),(2009,2010), and (0,2010)We need to find the probability that [tex]x>7y[/tex]So, Required Probability is given by[tex]\frac{\text{Area of triangle}}{\text{ Area of rectangle}}\\\\=\frac{0.5\times 2009\times 287}{2009\times 2010}\\\\=\frac{287}{4020}[/tex]Hence, Probability that [tex]x>7y[/tex] is [tex]\frac{287}{4020}[/tex]