If the total area of a dartboard is 20000 mm and the area of the bull's is 800 mm what is the probability of getting a bull's?

Answer 1

First of all an area is a measure in 2-dimensional space and so cannot be measured in mm which is a 1-dimensional measure. So the question is improper. However, assuming that you meant square mm, then the answer depends on the assumptions that you make.

First, you need, to assume that the player hits the board! You are looking for the conditional probability: the probability of hitting the bull conditional on hitting the board.

You could then assume that the player throws the dart in such a way that the probability of hitting a particular area is proportional to the size of that area, then the probability of hitting the bull is 0.04 or 4%.

You could instead assume that the player aims for the bull but has little control over how close the dart gets so that any distance from the centre is equally likely. Then the probability of hitting the bull is 0.2 or 20%.