The figure shows a smaller square within a larger square. A point is chosen at random inside the larger square. What is the probability that this point is in the shaded area? Write the answer as a decimal.
Given:
Side length of larger square = 10 in
Side length of smaller square = 5 in
To find:
The probability that this point is in the shaded area.
Solution:
Area of square formula =  side²
Area of larger square = 10²
                   = 100 in²
Area of smaller square = 5²
                   = 25 in²
Shaded area = Area of larger square - Area of smaller square
           = 100 in² - 25 in²
Shaded area = 75 in²
[tex]$\text{P(point in shaded area)}=\frac{\text{Shaded area}}{\text{Total area}}[/tex]
                   [tex]$=\frac{75}{100}[/tex]
                   = 0.75
The probability of point in shaded area is 0.75.