There are some circumstances under which it is convenient to estimate the smallest signal that can be detected reliably in order to set a “detection limit” for the counting system. Some regulatory agencies require that a certain minimum detectable amount (MDA) of activity be measurable while monitoring for the possible presence of radioactive contaminants. 

(i) Calculate the net counts when the real activity is present or not present in the sample. 

(ii) Also find the probability that exactly 12 heads will occur in 22 tosses of a coin