Chapter 10.3, Problem 8Q

a.

To determine

To calculate:

The probability of the center circle.

Answer to Problem 8Q

The probability of the center circle is $0.111$ .

Explanation of Solution

Given information:

  

Calculation:

The areas as per the question can be obtained as follows:

Calculate area of circle by using $\pi r^2$ ,

  Area of outer circle $=36\pi$

  Area of center circle $=4\pi$

Calculate area of square by using $a^2$ ,

  Area of square $=36$

Thus, the required probability measures are as follows:

The probability of a dart falling in the center circle is given,

  $\begin{array}{l}P\left(fallingoncentercircle\right)\\ =\frac{4\pi }{36\pi }\\ =0.111\end{array}$

Hence the probability of the center circle is $0.111$ .

b.

To determine

To calculate:

The probability of outside square.

Answer to Problem 8Q

The probability of outside squareis $0.3183$ .

Explanation of Solution

Given information:

  

Calculation:

The areas as per the question can be obtained as follows:

Calculate area of circle by using $\pi r^2$ ,

  Area of outer circle $=36\pi$

  Area of center circle $=4\pi$

Calculate area of square by using $a^2$ ,

  Area of square $=36$

Thus, the required probability measures are as follows:

The probability of a dart falling in the square is given,

  $\begin{array}{l}P\left(fallingoutsidesquare\right)\\ =\frac{36}{36\pi }\\ =0.3183\end{array}$

Hence the probability of outside square is $0.3183$ .

c.

To determine

To calculate:

The probability of inside the square but outside thecenter circle.

Answer to Problem 8Q

the probability of inside the square but outside the center circle is $0.2027$ .

Explanation of Solution

Given information:

  

Calculation:

The areas as per the question can be obtained as follows:

Calculate area of circle by using $\pi r^2$ ,

  Area of outer circle $=36\pi$

  Area of center circle $=4\pi$

Calculate area of square by using $a^2$ ,

  Area of square $=36$

Thus, the required probability measures are as follows:

The probability of inside the square but outside the center circle is given as,

  $\begin{array}{l}P\left(insidethesquarebutoutsidethecentercirclesquare\right)\\ =\frac{36-4\pi }{36\pi }\\ =0.2027\end{array}$ ,

Hence,the probability of inside the square but outside the center circle is $0.2027$ .