Chapter 13.3, Problem 4CYU

To determine

To calculate; to find the probability that archer will hit center.

Answer to Problem 4CYU

Solution: $P\left(archerhitscenter\right)=\frac{1}{100}or1\%$

Explanation of Solution

Probability of hitting the center can be found by comparing the area of center to that to the total area.

Since the diameter is decreasing by $12.2cm$ , the smallest circle which is center will have diameter of $12.2cm$

  $\begin{array}{l}r=\frac{d}{2}=\frac{12.2}{2}=6.1\\ Are{a}_{center}=\pi r^2=\pi {\left(6.1\right)}^2=37.21\pi \end{array}$

  $\begin{array}{l}r=\frac{d}{2}=\frac{122}{2}=61\\ Are{a}_{total}=\pi r^2=\pi {\left(61\right)}^2=3721\pi \end{array}$

  $\begin{array}{l}P\left(archerhitscenter\right)=\frac{areaofcenter}{totalarea}\\ =\frac{37.21\pi }{3721\pi }=\frac{37.21}{3721}=\frac{1}{100}=1\%\end{array}$

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