Answer: The probability of throwing a dart and hitting the white part of the board is 1.
Step-by-step explanation:
Since we have given that
Radius of shaded center circle = 1
So, Area of shaded center circle is given by
![\pi r^2\\\\=\pi \times 1^2\\\\=\pi](https://tex.z-dn.net/?f=%5Cpi%20r%5E2%5C%5C%5C%5C%3D%5Cpi%20%5Ctimes%201%5E2%5C%5C%5C%5C%3D%5Cpi)
Radius of entire dartboard = 4
Area of entire dartboard is given by
![\pi\times 4^2\\\\=16\pi](https://tex.z-dn.net/?f=%5Cpi%5Ctimes%204%5E2%5C%5C%5C%5C%3D16%5Cpi)
Area of white part is given by
![16\pi-\pi\\\\=15\pi](https://tex.z-dn.net/?f=16%5Cpi-%5Cpi%5C%5C%5C%5C%3D15%5Cpi)
So, Probability of throwing a dart and hitting the white part of the board is given by
![\dfrac{15\pi}{16\pi}\\\\\\=\dfrac{15}{16}=0.9375\approx 1](https://tex.z-dn.net/?f=%5Cdfrac%7B15%5Cpi%7D%7B16%5Cpi%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B15%7D%7B16%7D%3D0.9375%5Capprox%201)
Hence, the probability of throwing a dart and hitting the white part of the board is 1.