Chapter 13.3, Problem 34HP

To determine

To explain:

The reason for which of the solution is correct.

Answer to Problem 34HP

The Carter’s solution is correct.

Explanation of Solution

Given information:

  

Calculation:

  

The central angle of the shaded region is $360°$ .

Thus, the required angle can be given as:

  $\begin{array}{l}=360°-\left(125°+125°+60°\right)\\ =360°-310°\\ =50°\end{array}$

The probability that randomly chosen point within the circle will lie in the shaded region is:

  $\frac{50}{360}=13.9\%$

Reason for the above probability is:

The central angle of total region is $360°$ and the central angle of the sector required is $50°$ .

Hence the ratio of the above two angles is the required probability.

Thus, it is the option matching with Carter.

Hence, the Carter’s solution is correct.