Chapter 11.8, Problem 8WE

To determine

To Find: The probability that the parachutist avoid the two trees represented by circles in the diagram.

Answer to Problem 8WE

  $0.965$

Explanation of Solution

Given:

  

Length of landing area= $100m$

Width = $80m$

Area of landing area= $100\times 80m=8000m^2$

Area of two trees

  $\begin{array}{l}\pi r_1{}^2+\pi r_2{}^2\\ =3.14\times 5\times 5+3.14\times 8\times 8\\ =279.46m^2\end{array}$

Area of region without trees= area of landing area −area of two trees.

  $8000-279.46=7720.54m^2$

Probability that the parachutist avoid the two trees.

  $P=\frac{7720.54}{8000}=0.965$

Hence, the probability is $0.965$ .