The number of phone calls that Nicky receives on her mobile phone follows a Poisson process with a rate ???? = 3 calls per hour.

(i) Find the probability that she will receive three calls between 6:00 p.m. and 6:20 p.m.

(ii) Calculate the probability that she will receive three calls between 6:40 p.m.

and 7:00 p.m. and at least two calls between 7:10 p.m. and 7:30 p.m. on the same day.

(iii) Find the probability that she will receive three calls between 6:40 p.m. and 7:00 p.m. and at least six calls between 6:00 p.m. and 7:40 p.m. on the same day.