Question

1. Suppose a point is to be selected at random from the unit circle. Write the sample space associated with this random experiment.

Answer 1

Suppose (a,b) be  the centre of the circle .

then the sample space associated is ( [a-1,a+1] , [b-1,b+1] ) this means that x coordinate of the point from the unit circle can take any values from a-1 to a+1 and the y coordinate can take any values from b-1 to b+1 and the different combinations of each x and y coordinates make the sample space of this random experiment.  

Note : this is the sample space when any point ( even inside the unit circle) is also considered.