Question

Find the probability that a randomly chosen point is the figure lies in the shaded region. Give all answers in fraction and percent forms. help with #8

Answer 1

The probability that a randomly chosen point in the figure lies in the shaded region in percent form is

`\begin{gathered} p(chosen\text{ }a\text{ }shaded\text{ }region)=25\% \\ \\ \end{gathered}`

The probability that a randomly chosen point in the figure lies in the shaded region in fraction form is

`\begin{gathered} p(chosen\text{ }a\text{ }shaded\text{ }region)=(1)/(4) \\ \\ \end{gathered}`

Step-by-step explanation

To find the probability that a randomly chosen point in the figure lies in the shaded region, you need to first find the area of the shape (circle):

`Area\text{ }of\text{ }the\text{ }shape=\pi r^2`

The radius, r of the shape = 4

`Area\text{ }of\text{ }the\text{ }shape=3.14*4=50.24\text{ }squared\text{ }unit`

The next step is to find the area of the shaded region.

The radius of the shaded region = D/2 = 4/2 = 2

`Area\text{ }of\text{ }the\text{ }shaded\text{ }region=\pi r^2=3.14*2^2=12.56\text{ }square\text{ }unit`

Therefore, the probability that a randomly chosen point in the figure lies in the shaded region in fraction form is

`\begin{gathered} p(chosen\text{ }a\text{ }shaded\text{ }region)=\frac{Area\text{ }of\text{ }shaded\text{ }region}{Area\text{ }of\text{ }the\text{ }figure}=(12.56)/(50.24)=(1)/(4) \\ \\ \end{gathered}`

Also, the probability that a randomly chosen point in the figure lies in the shaded region in percent form is

`\begin{gathered} p(chosen\text{ }a\text{ }shaded\text{ }region)=(12.56)/(50.24)*100\%=(1)/(4)*100\%=25\% \\ \\ \end{gathered}`