Answer:
The probability that a randomly selected point within the circle falls in the red shaded area is p=0.75.
Step-by-step explanation:
We have to calculate the probability that a randomly selected point within the circle falls in the red shaded area.
This probability can be calculated as the quotient between the red shaded area, that is a regular pentagon inscribed in the circle, and the area of the circle.
We start by calculating the area of the circle:
[tex]A_c=\pi r^2\approx 3.14(4)^2=3.14\cdot 16=50.24[/tex]
Then, we can calculate the area of the pentagon as:
[tex]A_p=\dfrac{1}{2}\cdot (5a)\cdot S=\dfrac{1}{2}\cdot (5\cdot3.2)\cdot 4.7=37.6[/tex]
Then, we can calculate the probability p as the quotient between the areas:
[tex]p=\dfrac{A_p}{A_c}=\dfrac{37.6}{50.24}\approx 0.75[/tex]
