Chapter 11.8, Problem 3CE

To determine

To Find: The probability that the dart is within the outer circle and within the bull’s eye.

Answer to Problem 3CE

The probability that the dart is within the outer circle is $0.50$ .

The probability that the dart is within the bull’s eye is $0.0314$ .

Explanation of Solution

Given:

  

Probability of dart landing in outer circle.

  $\begin{array}{l}P=\frac{\text{area of circle}}{\text{area of square}}\\ P=\frac{\pi r^2}{s^2}\\ P=\frac{3.14\times 4\times 4}{10\times 10}\\ P=0.50\end{array}$

Probability of dart landing within bull’s eye.

  $\begin{array}{l}P=\frac{\text{area of inner circle}}{\text{area of square}}\\ P=\frac{\pi r^2}{s^2}\\ P=\frac{3.14\times 1\times 1}{10\times 10}\\ P=0.0314\end{array}$

Hence,

The probability that the dart is within the outer circle is $0.50$ .

The probability that the dart is within the bull’s eye is $0.0314$ .