Question

12. What is the probability that a point in the square below

is in the shaded region? Write your answer as a
percent.

Answer 1

`21.5\%`

Explanation:

we know that

The probability that a point in the square below is in the shaded region, is equal to divide the area of the shaded region by the area of the square

step 1

Find the area of the shaded region

The area is equal to the area of the square minus the area of the circle

`A=b^(2) -\pi(r)^(2)`

we have

`b=12\ cm` ---> length side of the square

`r=12/2=6\ cm` ----> the radius is half the diameter

assume

`\pi =3.14`

substitute

`A=12^(2) -(3.14)(6)^(2)`

`A=30.96\ cm^(2)`

step 2

Find the area of the square

`A=b^(2)`

we have

`b=12\ cm` ---> length side of the square

substitute

`A=12^(2)=144\ cm^(2)`

step 3

Find the probability

`P=30.96/144=0.215`

Convert to percent form

`0.215*100=21.5\%`