We are given two squares and we know that the probability of a randomly chosen point falling into the shaded region of either of them is the same.
To show that these probabilities are the same we will calculate them. To do this we should use the geometric probability and divide the area of the shaded region by the area of the square. Let's start with the first square.
The area of the first square is 1^2= 1 square inches. To calculate the area of the shaded region we should subtract the area of the smaller square from the area of the greater square.
1- 0.75^2=0.4375
The area of the shaded region for the first square is 0.4375 square inches. Notice that this is the same as the area of the shaded region in the second square.
Since both squares have the same area and the areas of their shaded regions are equal, the probabilities also must be the same.
0.4375/1^2=0.4375/1^2
