Question

Acellus

Answer 1

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:

$A_c=\pi r^2\approx 3.14(4)^2=3.14\cdot 16=50.24$

Then, we can calculate the area of the pentagon as:

$A_p=\dfrac{1}{2}\cdot (5a)\cdot S=\dfrac{1}{2}\cdot (5\cdot3.2)\cdot 4.7=37.6$

Then, we can calculate the probability p as the quotient between the areas:

$p=\dfrac{A_p}{A_c}=\dfrac{37.6}{50.24}\approx 0.75$