Chapter 13.3, Problem 30PPS

To determine

To calculate:

The probability that point chosen at the random lies in shaded region:

Answer to Problem 30PPS

The probability of the point chosen at the random lies in shaded region is $0.21$ .

Explanation of Solution

Given information:

  

Calculation:

The area of rectangle is the product of the side length of rectangle. For a rectangle with the side length of $12$ and $18$ :

The area of rectangle:

  $\begin{array}{l}=12\times 18\\ =216{\text{units}}^2\end{array}$

The area of circle with the radius $r$ equal to $\pi r^2$ .

The area of the sum of six circles with radius three is

  $\begin{array}{l}=6\left(\pi 3^2\right)\\ =54\pi {\text{units}}^2\end{array}$

The probability that point chosen at the random lies in shaded region by dividing the area of shaded region by the area of given figure:

  $P\left(A\right)$ : P (Point lies in shaded region)

  $A$ : Area of shaded region

  $S$ : Area of entire region

  $\begin{array}{l}P\left(A\right)=\frac{A}{S}\\ P\left(A\right)=\frac{216-54\pi }{216}\\ P\left(A\right)=\frac{46.35}{216}\\ P\left(A\right)=0.21\end{array}$

The probability of the point chosen at the random lies in shaded region is $0.21$ .