Chapter 11.8, Problem 7WE

To determine

To Find: The probability that the dart that hits the board will also hit the balloon.

Answer to Problem 7WE

  $0.0157$

Explanation of Solution

Given: A dart is thrown at a board of $12m$ long and $5m$ wide. Attached to the boards are $30ballons$ with a radius of $10cm$ .

Length of board= $12m$

Width = $5m$

Area of board= $12\times 5m=60m^2$

Area of one balloon = $\pi r^2=3.14\times 0.10\times 0.10=0.0314m^2$

Area of $30ballons$

  $30\times 0.0314=0.942m^2$

Probability that dart hits the board will also hit the balloon.

  $\begin{array}{l}P=\frac{ar(30balloons)}{ar(board)}\\ P=\frac{0.942}{60}=0.0157\end{array}$

Hence, the probability is $0.0157$ .