circle inside square, Square side length is 4 it's the probablity it will land in the square and not the circle

Question

express the answer in precentage to he nearest tenth 

Answer 1

So we have a circle inscribed within the square, and we are only given the square sides' length as 4.

 

We need to find the probability of hitting only the square not circle areas. In probability, all of the event space is equal to 100%, nothing less or more. So the problem assumes you will have no chance of hitting outside the square.

 

Given the areas of a square and circle and the above:

1. A_square=b*b
2. b=4
3. A_circle=π*r²
4. 2*r=b (diameter of circle touching the squares sides)

 

Then the probability of hitting the square target area not the circle is:

1-(A_circle/A_square) and rounded to the nearest tenth.