Chapter 10.1, Problem 13E

To determine

To calculate:

Probability that your dart lands in yellow region.

Answer to Problem 13E

The probability of your dart lands in yellow region is $0.587$ .

Explanation of Solution

Given information:

  

Calculation:

The question is related to the favorable event.

Possible event that it is designated region o hitting of given dart is shown in calculation as below:

  $\begin{array}{l}\pi \times 81-2\times \frac{1}{2}\times 6\times 6-\pi \times 9\\ =\pi \times 72-36\\ =\frac{18-6}{2}\\ =6\end{array}$

The total area under consideration is on the other hand,

  $\begin{array}{l}=18\times 18\\ =324\end{array}$

Hence the probability of the event taken into the consideration of hitting thedart in designated yellow region is,

  $P$ (Hitting)

  $\begin{array}{l}=\frac{72\pi -36}{324}\\ =0.587\end{array}$

Hence, the probability of your dart lands in yellow region is $0.587$ .