Irene has a Facebook page and she is very keen to have a large number of friends there. The number of friends added to her page follows a Poisson process with a rate of ???? = 3 persons per week.

(i) What is the probability that on a particular week she makes less than three new friends?

(ii) Find how long she has to wait from now on so that she makes at least one new friend with a probability of 99%.

(iii) Suppose that during a particular week she made no new friends between Sunday and Friday, and so on Friday night she felt very disappointed and wanted to know the probability that there would be at least one new friend on Saturday of that week. Can you give an answer to her question?