It has been observed that the number of particles emitted by a radioactive substance which reach a given portion of space during time t follows closely the Poisson distribution with parameter l. Calculate the probability that:
i) No particles reach the portion of space under consideration during time t;
ii) Exactly 120 particles do so;
iii) At least 50 particles do so;
iv) Give the numerical values in (i)-(iii) if l = 100.