A digital scale has an accuracy of two decimal places shown on its screen. Each time a person steps on the scale, we record his/her weight by rounding it to the closest integer (in kilograms). Thus, if the decimal part is 0.50 or greater, we round up to the next integer.

(i) Give an appropriate sample space for the experiment whose outcome is the rounding error during the above procedure.

(ii) Write explicitly each of the events A: the rounding error is at most 0.10;

B: the absolute value of the rounding error is at least 0.20.