If the radius of the shaded center circle is 2 and the radius of the entire dartboard is 4, what is the probability of throwing a dart and hitting the white part of the board? Round your answer to the nearest whole number.
In a blind throw, and assuming the dart must hit the board, the probability of hitting the shaded centre is 25%.
Since area is proportional to
So, the shaded area is only one-fourth of the larger area, and the probability of hitting it would appear to be one fourth (25%) as well.
It is not clear from the question, which the 'white' part of the board is. However, as the middle circle is 'shaded', I assume that the white part is the unshaded part.
It is possible to find the comparison between the areas of the shaded and white parts without doing the whole calculations, but working just in terms of
Area shaded circle:
Area of the entire board:
The white area is given by
So, with a random throw which does hit the board,: