Question

If the radius of the shaded center circle is 1 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?

67%
34%
94%
6%

Answer 1

We should re-phrase the question a bit :)

If you were to throw a dart at the board, and the dart was absolutely guaranteed to land somewhere inside the entire dartboard area, then the dart has as its target area: `A_{"Total"} = pi 4^2 = 16 pi`.

And if the actual destination of the dart within that entire `16 pi` area is totally random , ie it can land anywhere with equal probability, then we note that:

• the inner shaded area is `A_("Inner") = pi 1^2 = pi`.

• the remaining area is `A_("Outer") = 15pi`.

So, the odds of hitting a white-shaded (non-blue) area is:

• `(15pi)/(16 pi) = 15/16`.