Find the probability by looking at the ratio of the area of the shaded region to the area of the square.
A
Practice makes perfect
To find the probability, we need find the ratio of the favorable shaded region's area to the total area of the square. Take note that the region which is not shaded is formed by 4 identical circles. This means that the area of the shaded region is the area of the square minus the area of the circles.
A_(Shaded Region)= A_(Square) -4A_(Circle)
In the image, we can see that two circles fit exactly across the width of the square. Since the square has a width of 4, the diameter of each circle is 2. This means that the radius of each circle is 1. Knowing the radius, we can now find the area of one of the circles.
A_(Circle)&= π r^2
&=π (1)^2
&=π
Now, we just need to find the area of the square with a side length of 4.
A_(Square)&= s^2
&=(4)^2
&= 16
Now, let's find the area of the shaded region using the formula we created earlier.
The area of the favorable shaded region is about 3.43 m^2. We can now find the probability of landing in the favorable shaded region by comparing the area of that region with area of the entire square.
P=Shaded Region/Square=3.43/16
The probability of landing in the shaded region is 3.4316 or about 21 % which closest to choice A.
